case study ch 7 class 10 maths

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CBSE Class 10 Maths Case Study Questions for Chapter 7 - Coordinate Geometry (Released By CBSE)

Cbse's question bank on case study for class 10 maths chapter 7 is available here. practice this new type of questions to score good marks in your board exam..

Case study based questions for CBSE Class 10 Maths Chapter 7 - Coordinate Geometry are provided here for students to practice this new format of questions for their Maths Board Exam 2022. All these questions are published by the Central Board of Secondary Education (CBSE) for Class 10 Maths. Students must solve these questions to familiarise themselves with the concepts and logic used in the case study. You can also check the right answer at the end of each question.

Check Case Study Questions for Class 10 Maths Chapter 7 - Coordinate Geometry

CASE STUDY 1:

In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD, 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in given figure below. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th distance AD on the eighth line and posts a red flag.

1. Find the position of green flag

b) (2,0.25)

d) (0, -25)

Answer:  a) (2,25)

2. Find the position of red flag

Answer: c) (8,20)

3. What is the distance between both the flags?

a) √41

b) √11

c) √61

d) √51

Answer: c) √61

4. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

a) (5, 22.5)

d) (2.5,20)

Answer: a) (5, 22.5)

5. If Joy has to post a flag at one-fourth distance from green flag , in the line segment joining the green and red flags, then where should he post his flag?

a) (3.5,24)

b) (0.5,12.5)

c) (2.25,8.5)

Answer: a) (3.5,24)

CASE STUDY 2:

The class X students school in krishnagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.

1. Taking A as origin, find the coordinates of P

Answer: a) (4,6)

2. What will be the coordinates of R, if C is the origin?

Answer: c) (10,3)

3. What will be the coordinates of Q, if C is the origin?

b) b) (-6,13)

Answer: d) (13,6)

4. Calculate the area of the triangles if A is the origin

Answer: a) 4.5

5. Calculate the area of the triangles if C is the origin

Answer: d) 4.5

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Class 10 Maths Case Study Questions Chapter 7 Coordinate Geometry

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Case study Questions in the Class 10 Mathematics Chapter 7  are very important to solve for your exam. Class 10 Maths Chapter 7 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving  Class 10 Maths Case Study Questions  Chapter 7  Coordinate Geometry

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Coordinate Geometry Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 7 Coordinate Geometry

Case Study/Passage-Based Questions

Question 1:

Answer: (d) none of these

(ii) The distance of the bus stand from the house is

Answer: (b) 10 cm

(iii) If the grocery store and electrician’s shop lie on a line, the ratio of the distance of the house from the grocery store to that from the electrician’s shop, is

Answer: (c) 1.2

(iv) The ratio of distances of the house from the bus stand to food cart is

Answer: (c) 1.1

(v) The coordinates of positions of bus stand, grocery store, food cart, and electrician’s shop form a

Question 2:

The class X student’s school in krishnagar has been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.

1. Taking A as origin, find the coordinates of P

Answer: a) (4,6)

2. What will be the coordinates of R, if C is the origin?

Answer: c) (10,3)

3. What will be the coordinates of Q, if C is the origin?

b) b) (-6,13)

Answer: d) (13,6)

4. Calculate the area of the triangles if A is the origin

Answer: a) 4.5

5. Calculate the area of the triangles if C is the origin

Answer: d) 4.5

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 7 Coordinate Geometry with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Coordinate Geometry Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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Class 10 Maths Chapter 7 Case Based Questions - Coordinate Geometry

Study case - 1.

The class X students of a school in Rajinder Nagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Mango are planted on the boundary at the distance of 1 m from each other.

Based on the above figure, answer the following questions:

  Q4: What will be the coordinates of the vertices of ΔPQR if C is the origin? (a) (14, 3), (11, 2), (8, 6) (b) (15, 4), (12, 3), (9, 7) (c) (14, 2), (11, 1), (8, 5) (d) (15, 3), (12, 2), (9, 6) Ans:  (d) Explanation:  When C is taken as origin, we will take CB as X-axis and CD as Y-axis. Then, coordinates of points, P, Q and R are (15, 3), (12, 2)and (9, 6) respectively.

Q5: What are the coordinates of P if D is taken as the origin? (a) (−15, 5) (b) (15, 5) (c) (15, 7) (d) (15, 3) Ans:  (a) Explanation:  When D is taken as origin, we will take DA as negative X-axis and DC as positive Y-axis.   Then coordinates of point P is (−15, 5).

Case Study - 2

Based on the above information, give the answer of the following questions: 

Study Case - 3

Based on the above information give the answer of the following questions:

Q1: The coordinates of the point A are: (a) (4,9) (b) (5,9) (c) (92,9) (d) (4,8) Ans: (c) Explanation:  As the distance of point A is 9/2 units from the Y-axis and 9 units from the X-axis, its coordinates are x = 9/2, y = 9 or (9/2, 9)

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Chapter 7 Class 10 Coordinate Geometry

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Get NCERT Solutions of all Exercise Questions and Examples of Chapter 7 Class 10 Coordinate Geometry. All questions have been solved in an easy to understand way with detailed explanation of each and every step.

Answers to optional exercise is also given

In Coordinate Geometry of Class 9, we learned what is x and y coordinate of a point. 

In this chapter, we will learn 

• Coordinates of points in x-axis (x, 0) and y-axis (0, y)
• How to find distance between two points using Distance Formula
• Checking if points form a triangle, or an isoceles triangle, or a square, rectangle. (To do this, we need to learn properties of parallelogram )
• Checking if 3 points are collinear using Distance Formula
• Finding points equidistant to given points
• Then, we will learn about Section Formula - Finding coordinates of a point that divides line joining two points in some ratio
• Finding coordinates of mid-point of a line using Section Formula
• Finding ratio when coordinates of point of intersection is given
• Using properties of parallelogram to do some questions on Section Formula (like finding coordinates of a point, when 4 vertices of parallelogram are given)
• Finding Area of triangle when coordinates of all 3 vertices are given
• Proving 3 points collinear using Area of Triangle Formula
• Finding Area of Quadrialteral using Area of Triangle Formula (dividing Quadrilateral into 2 triangles and finding area)

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CBSE Class 10 Maths: Case Study Questions of Chapter 7 Coordinate Geometry PDF Download

Case study Questions in the Class 10 Mathematics Chapter 7  are very important to solve for your exam. Class 10 Maths Chapter 7 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based   questions for Class 10 Maths Chapter 7  Coordinate Geometry

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on  Assertion and Reason . There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Coordinate Geometry Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 7 Coordinate Geometry

Case Study/Passage-Based Questions

Question 1:

Answer: (d) none of these

(ii) The distance of the bus stand from the house is

Answer: (b) 10 cm

(iii) If the grocery store and electrician’s shop lie on a line, the ratio of the distance of the house from the grocery store to that from the electrician’s shop, is

Answer: (c) 1.2

(iv) The ratio of distances of the house from the bus stand to food cart is

Answer: (c) 1.1

(v) The coordinates of positions of bus stand, grocery store, food cart, and electrician’s shop form a

Question 2:

The class X student’s school in krishnagar has been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.

1. Taking A as origin, find the coordinates of P

Answer: a) (4,6)

2. What will be the coordinates of R, if C is the origin?

Answer: c) (10,3)

3. What will be the coordinates of Q, if C is the origin?

b) b) (-6,13)

Answer: d) (13,6)

4. Calculate the area of the triangles if A is the origin

Answer: a) 4.5

5. Calculate the area of the triangles if C is the origin

Answer: d) 4.5

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 7 Coordinate Geometry with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Coordinate Geometry Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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Now, CBSE will ask only subjective questions in class 10 Maths case studies. But if you search over the internet or even check many books, you will get only MCQs in the class 10 Maths case study in the session 2022-23. It is not the correct pattern. Just beware of such misleading websites and books.

We advise you to visit CBSE official website ( cbseacademic.nic.in ) and go through class 10 model question papers . You will find that CBSE is asking only subjective questions under case study in class 10 Maths. We at myCBSEguide helping CBSE students for the past 15 years and are committed to providing the most authentic study material to our students.

Here, myCBSEguide is the only application that has the most relevant and updated study material for CBSE students as per the official curriculum document 2022 – 2023. You can download updated sample papers for class 10 maths .

First of all, we would like to clarify that class 10 maths case study questions are subjective and CBSE will not ask multiple-choice questions in case studies. So, you must download the myCBSEguide app to get updated model question papers having new pattern subjective case study questions for class 10 the mathematics year 2022-23.

Class 10 Maths has the following chapters.

• Real Numbers Case Study Question
• Polynomials Case Study Question
• Pair of Linear Equations in Two Variables Case Study Question
• Quadratic Equations Case Study Question
• Arithmetic Progressions Case Study Question
• Triangles Case Study Question
• Coordinate Geometry Case Study Question
• Introduction to Trigonometry Case Study Question
• Some Applications of Trigonometry Case Study Question
• Circles Case Study Question
• Area Related to Circles Case Study Question
• Surface Areas and Volumes Case Study Question
• Statistics Case Study Question
• Probability Case Study Question

Format of Maths Case-Based Questions

CBSE Class 10 Maths Case Study Questions will have one passage and four questions. As you know, CBSE has introduced Case Study Questions in class 10 and class 12 this year, the annual examination will have case-based questions in almost all major subjects. This article will help you to find sample questions based on case studies and model question papers for CBSE class 10 Board Exams.

Maths Case Study Question Paper 2023

Here is the marks distribution of the CBSE class 10 maths board exam question paper. CBSE may ask case study questions from any of the following chapters. However, Mensuration, statistics, probability and Algebra are some important chapters in this regard.

Case Study Question in Mathematics

Here are some examples of case study-based questions for class 10 Mathematics. To get more questions and model question papers for the 2021 examination, download myCBSEguide Mobile App .

Case Study Question – 1

In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021–22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year.

• Find the production in the 1 st year.
• Find the production in the 12 th year.
• Find the total production in first 10 years. OR In which year the total production will reach to 15000 cars?

Case Study Question – 2

In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.

• Find the distance between Lucknow (L) to Bhuj(B).
• If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
• Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P) OR Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).

Case Study Question – 3

• Find the distance PA.
• Find the distance PB
• Find the width AB of the river. OR Find the height BQ if the angle of the elevation from P to Q be 30 o .

Case Study Question – 4

• What is the length of the line segment joining points B and F?
• The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z?
• What are the coordinates of the point on y axis equidistant from A and G? OR What is the area of area of Trapezium AFGH?

Case Study Question – 5

The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

• If the first circular row has 30 seats, how many seats will be there in the 10th row?
• For 1500 seats in the auditorium, how many rows need to be there? OR If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after 10 th row?
• If there were 17 rows in the auditorium, how many seats will be there in the middle row?

Case Study Question – 6

• Draw a neat labelled figure to show the above situation diagrammatically.

• What is the speed of the plane in km/hr.

More Case Study Questions

We have class 10 maths case study questions in every chapter. You can download them as PDFs from the myCBSEguide App or from our free student dashboard .

As you know CBSE has reduced the syllabus this year, you should be careful while downloading these case study questions from the internet. You may get outdated or irrelevant questions there. It will not only be a waste of time but also lead to confusion.

Here, myCBSEguide is the most authentic learning app for CBSE students that is providing you up to date study material. You can download the myCBSEguide app and get access to 100+ case study questions for class 10 Maths.

How to Solve Case-Based Questions?

Questions based on a given case study are normally taken from real-life situations. These are certainly related to the concepts provided in the textbook but the plot of the question is always based on a day-to-day life problem. There will be all subjective-type questions in the case study. You should answer the case-based questions to the point.

What are Class 10 competency-based questions?

Competency-based questions are questions that are based on real-life situations. Case study questions are a type of competency-based questions. There may be multiple ways to assess the competencies. The case study is assumed to be one of the best methods to evaluate competencies. In class 10 maths, you will find 1-2 case study questions. We advise you to read the passage carefully before answering the questions.

Case Study Questions in Maths Question Paper

CBSE has released new model question papers for annual examinations. myCBSEguide App has also created many model papers based on the new format (reduced syllabus) for the current session and uploaded them to myCBSEguide App. We advise all the students to download the myCBSEguide app and practice case study questions for class 10 maths as much as possible.

Case Studies on CBSE’s Official Website

CBSE has uploaded many case study questions on class 10 maths. You can download them from CBSE Official Website for free. Here you will find around 40-50 case study questions in PDF format for CBSE 10th class.

10 Maths Case Studies in myCBSEguide App

You can also download chapter-wise case study questions for class 10 maths from the myCBSEguide app. These class 10 case-based questions are prepared by our team of expert teachers. We have kept the new reduced syllabus in mind while creating these case-based questions. So, you will get the updated questions only.

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NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry

NCERT Solutions Class 10 Maths Chapter 7 Coordinate Geometry are provided here to help the students of CBSE class 10. Our expert teachers prepared all these solutions as per the latest CBSE syllabus and guidelines. In this chapter, we have discussed the similarity of triangles, criterion for similarity of triangles, areas of similar triangles and Pythagoras theorem. CBSE Class 10 Maths solutions provide a detailed and step-wise explanation of each answer to the questions given in the exercises of NCERT books.

CBSE Class 10 Maths Chapter 7 Coordinate Geometry Solutions

Below we have given the answers to all the questions present in Coordinate Geometry in our NCERT Solutions for Class 10 Maths chapter 7. In this lesson, students are introduced to a lot of important concepts that will be useful for those who wish to pursue mathematics as a subject in their future classes. Based on these solutions, students can prepare for their upcoming Board Exams. These solutions are helpful as the syllabus covered here follows NCERT guidelines.

NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.1

NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.2

NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.3

NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.4

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Case Study Class 10 Maths Questions and Answers (Download PDF)

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Case Study Class 10 Maths

If you are looking for the CBSE Case Study class 10 Maths in PDF, then you are in the right place. CBSE 10th Class Case Study for the Maths Subject is available here on this website. These Case studies can help the students to solve the different types of questions that are based on the case study or passage.

CBSE Board will be asking case study questions based on Maths subjects in the upcoming board exams. Thus, it becomes an essential resource to study. 

The Case Study Class 10 Maths Questions cover a wide range of chapters from the subject. Students willing to score good marks in their board exams can use it to practice questions during the exam preparation. The questions are highly interactive and it allows students to use their thoughts and skills to solve the given Case study questions.

Download Class 10 Maths Case Study Questions and Answers PDF (Passage Based)

Download links of class 10 Maths Case Study questions and answers pdf is given on this website. Students can download them for free of cost because it is going to help them to practice a variety of questions from the exam perspective.

Case Study questions class 10 Maths include all chapters wise questions. A few passages are given in the case study PDF of Maths. Students can download them to read and solve the relevant questions that are given in the passage.

Students are advised to access Case Study questions class 10 Maths CBSE chapter wise PDF and learn how to easily solve questions. For gaining the basic knowledge students can refer to the NCERT Class 10th Textbooks. After gaining the basic information students can easily solve the Case Study class 10 Maths questions.

Case Study Questions Class 10 Maths Chapter 1 Real Numbers

Case Study Questions Class 10 Maths Chapter 2 Polynomials

Case Study Questions Class 10 Maths Chapter 3 Pair of Equations in Two Variables

Case Study Questions Class 10 Maths Chapter 4 Quadratic Equations

Case Study Questions Class 10 Maths Chapter 5 Arithmetic Progressions

Case Study Questions Class 10 Maths Chapter 6 Triangles

Case Study Questions Class 10 Maths Chapter 7 Coordinate Geometry

Case Study Questions Class 10 Maths Chapter 8. Introduction to Trigonometry

Case Study Questions Class 10 Maths Chapter 9 Some Applications of Trigonometry

Case Study Questions Class 10 Maths Chapter 10 Circles

Case Study Questions Class 10 Maths Chapter 12 Areas Related to Circles

Case Study Questions Class 10 Maths Chapter 13 Surface Areas & Volumes

Case Study Questions Class 10 Maths Chapter 14 Statistics

Case Study Questions Class 10 Maths Chapter 15 Probability

How to Solve Case Study Based Questions Class 10 Maths?

In order to solve the Case Study Based Questions Class 10 Maths students are needed to observe or analyse the given information or data. Students willing to solve Case Study Based Questions are required to read the passage carefully and then solve them. 

While solving the class 10 Maths Case Study questions, the ideal way is to highlight the key information or given data. Because, later it will ease them to write the final answers. 

Case Study class 10 Maths consists of 4 to 5 questions that should be answered in MCQ manner. While answering the MCQs of Case Study, students are required to read the paragraph as they can get some clue in between related to the topics discussed.

Also, before solving the Case study type questions it is ideal to use the CBSE Syllabus to brush up the previous learnings.

Features Of Class 10 Maths Case Study Questions And Answers Pdf

Students referring to the Class 10 Maths Case Study Questions And Answers Pdf from Selfstudys will find these features:-

• Accurate answers of all the Case-based questions given in the PDF.
• Case Study class 10 Maths solutions are prepared by subject experts referring to the CBSE Syllabus of class 10.
• Free to download in Portable Document Format (PDF) so that students can study without having access to the internet.

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Since, CBSE Class 10 Maths Case Study Questions and Answers are prepared by our maths experts referring to the CBSE Class 10 Syllabus, it provided benefits in various way:-

• Case study class 10 maths helps in exam preparation since, CBSE Class 10 Question Papers contain case-based questions.
• It allows students to utilise their learning to solve real life problems.
• Solving case study questions class 10 maths helps students in developing their observation skills.
• Those students who solve Case Study Class 10 Maths on a regular basis become extremely good at answering normal formula based maths questions.
• By using class 10 Maths Case Study questions and answers pdf, students focus more on Selfstudys instead of wasting their valuable time.
• With the help of given solutions students learn to solve all Case Study questions class 10 Maths CBSE chapter wise pdf regardless of its difficulty level.

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• Math Article
• Coordinate Geometry For Class 10

Coordinate Geometry Class 10 Notes

Cbse class 10 maths coordinate geometry notes:- download pdf here, class 10 maths chapter 7 coordinate geometry notes.

The complete notes on coordinate geometry for Class 10 are provided here. Coordinate geometry teaches us the location of a point on a plane. For example, the coordinates of a point are (x, y), where x-coordinate (abscissa) denotes the distance of a point from the y-axis and y-coordinate (ordinate) denotes the distance of the point from the x-axis. Now we will learn to find the distance between two points and the area of a triangle using the distance formula when the coordinates of the points are given. Go through the below article and learn the points on the coordinate plane, distance formulas, section formulas and so on with a detailed explanation.

Students can refer to the short notes and MCQ questions along with a separate solution pdf of this chapter for quick revision from the links below:

• Coordinate Geometry Short Notes
• Coordinate Geometry MCQ Practice Questions
• Coordinate Geometry MCQ Practice Solutions

Basics of Coordinate Geometry

For more information on the basics of coordinate geometry, watch the below video.

To know more about Coordinate Geometry, visit here .

Points on a Cartesian Plane

A pair of numbers locate points on a plane called the coordinates . The distance of a point from the y-axis is known as  abscissa or x-coordinate. The distance of a point from the x-axis is called  ordinate or y-coordinate.

Example: Consider a point P(3, 2), where 3 is the abscissa, and 2 is the ordinate. 3 represents the distance of point P from the y-axis, and 2 represents the distance of point P from the x-axis.

Distance Formula

Distance between two points on the same coordinate axes.

The distance between two points that are on the same axis (x-axis or y-axis) is given by the difference between their ordinates if they are on the y-axis, else by the difference between their abscissa if they are on the x-axis.

Distance AB = 6 – (-2) = 8 units

Distance CD = 4 – (-8) = 12 units

Distance between Two Points Using Pythagoras Theorem

Let P(x 1 , y 1 ) and Q(x 2 , y 2 ) be any two points on the cartesian plane.

Draw lines parallel to the axes through P and Q to meet at T.

ΔPTQ is right-angled at T.

By  Pythagoras Theorem ,

PQ 2  = PT 2  + QT 2

= (x 2  – x 1 ) 2  + (y 2  – y 1 ) 2

Distance between any two points (x 1 , y 1 ) and (x 2 , y 2 ) is given by

Where d is the distance between the points (x 1 ,y 1 ) and (x 2 ,y 2 ).

To know more about Distance Formula, visit here .

Section Formula

If the point P(x, y) divides the line segment joining A(x 1 , y 1 ) and B(x 2 , y 2 ) internally  in the ratio m:n , then, the coordinates of P are given by the section formula as:

For more information on Section Formula, watch the below video

To know more about Section Formula, visit here .

Finding Ratio given the points

To find the ratio in which a given point P(x, y) divides the line segment joining A(x 1 , y 1 ) and B(x 2 , y 2 ),

• Assume that the ratio is k : 1
• Substitute the ratio in the section formula for any of the coordinates to get the value of k.

When x1, x2 and x are known, k can be calculated. The same can be calculated from the y- coordinate also.

Example: Find the ratio when point (– 4, 6) divide the line segment joining the points A(– 6, 10) and B(3, – 8)?

Solution: Let the ratio be m:n.

We can write the ratio as:

m/n : 1 or k:1

Suppose (-4, 6) divide the line segment AB in k:1 ratio.

Now using the section formula, we have the following;

-4 = (3k-6)/(k+1)

– 4k – 4 = 3k – 6

k : 1 = 2 : 7

Thus, the required ratio is 2:7.

The midpoint of any line segment divides it in the ratio 1 : 1 .

The coordinates of the midpoint(P) of line segment joining A(x 1 , y 1 ) and B(x 2 , y 2 ) is given by

Example: What is the midpoint of line segment PQ whose coordinates are P (-3, 3) and Q (1, 4), respectively.

Solution: Given,  P (-3, 3) and Q (1, 4) are the points of line segment PQ.

Using midpoint formula, we have;

= (-2/2, 1/2)

= (-1, 1/2)

Points of Trisection

To find the points of trisection P and Q, which divides the line segment joining A(x 1 , y 1 ) and B(x 2 , y 2 ) into three equal parts:

i) AP : PB = 1 : 2

ii)  AQ : QB = 2 : 1

Example: Find the coordinates of the points of trisection of the line segment joining the points A(2, – 2) and B(– 7, 4).

Solution: Let P and Q divide the line segment AB into three parts.

So, P and Q are the points of trisection here.

Let P divides AB in 1:2, thus by section formula, the coordinates of P are (1, 0)

Let Q divides AB in 2:1 ratio, then by section formula, the coordinates are (-4,2)

Thus, the point of trisection for line segment AB are (1,0) and (-4,2).

Centroid of a Triangle

If A(x 1 , y 1 ), B(x 2 , y 2 ), and C(x 3 , y 3 ) are the vertices of a ΔABC, then the coordinates of its centroid(P) are given by

Example: Find the coordinates of the centroid of a triangle whose vertices are given as (-1, -3), (2, 1) and (8, -4)

Solution: Given,

The coordinates of the vertices of a triangle are (-1, -3), (2, 1) and (8, -4)

The Centroid of a triangle is given by:

G = ((x 1 +x 2 +x 3 )/3 , (y 1 +y 2 +y 3 )/3 )

G = ((-1+2+8)/3 , (-3+1-4)/3)

G =( 9/3 , -6/3)

G = (3, -2)

Therefore, the centroid of a triangle, G = (3, -2)

Learn more:  Centroid of a Triangle

Area from Coordinates

Area of a triangle given its vertices.

If A(x 1 , y 1 ),B(x 2 , y 2 ) and C(x 3 , y 3 ) are the vertices of a Δ ABC, then its area is given by

Where A is the area of the Δ ABC.

Example: Find the area of the triangle ABC whose vertices are A(1, 2), B(4, 2) and C(3, 5).

Using the formula given above,

Area = 9/2 square units.

Therefore, the area of a triangle ABC is 9/2 square units.

To know more about the Area of a Triangle, visit here .

Collinearity Condition

If three points A, B and C are collinear and B lies between A and C, then,

• AB + BC = AC. AB, BC, and AC can be calculated using the distance formula.
• The ratio in which B divides AC, calculated using the section formula for both the x and y coordinates separately, will be equal.
• The area of a triangle formed by three collinear points is zero.

Video Lesson on Coordinate Geometry Toughest Problems

Coordinate Geometry for Class 10 Problems

Determine the distance between the pair of points (a, b) and (-a, -b)

Let the given points be A(a, b) and B(-a, -b)

We know that the distance formula is:

AB = √[(x 2 -x 1 ) 2 +(y 2 -y 1 ) 2 ]

(x 1 , y 1 ) = (a, b)

(x 2 , y 2 ) = (-a, -b)

Now, substitute the values in the distance formula, we get

AB = √[(-a-a) 2 +(-b-b) 2 ]

AB = √[(-2a) 2 + (-2b) 2 ]

AB = √[4a 2 +4b 2 ]

AB = √[4(a 2 +b 2 )]

AB = √4. √[a 2 +b 2 ]

AB = 2.√[a 2 +b 2 ].

Hence, the distance between two points (a, b) and (-a, -b) is 2√[a 2 +b 2 ].

Determine the ratio in which the line segment joining the points A(1, -5) and B(-4, 5) is divided by the x-axis. Also, find the coordinates of the point of division.

Given that, the point P is on the x-axis. Hence, the y-coordinate is 0. Hence, the point is of the form P(x, 0).

Now, we have to find the ratio. Let the ratio be k:1.

Given Points: A(1, -5) and B = (-4, 5).

(x 1 , y 1 ) = (1, -5)

(x 2 , y 2 ) = (-4, 5)

m 1 = k, m 2 = 1

We know that the section formula is:

y= [m 1 y 2 +m 2 y 1 ]/[m 1 +m 2 ]

Now, substitute the values in the section formula, we get

y = [k(5) + 1(-5)]/[k+1]

y = [5k-5]/[k+1]

(5k-5)/(k+1) = 0

Hence, the ratio k:1 = 1:1

Finding x-coordinate:

x= [m 1 x 2 +m 2 x 1 ]/[m 1 +m 2 ]

x = [k(-4) + 1(1)]/(k+1)

Now, substitute k=1 in the above equation, we get

x = [1(-4) + 1(1)]/(1+1)

x = (-4+1)/2

Hence, the coordinate of the point is P(x, 0) = P(-3/2, 0).

Related Articles

• NCERT Solutions for Class 10 Chapter 7 Coordinate Geometry
• Class 10 Maths Chapter 7 Coordinate Geometry MCQs
• Important Questions Class 10 Maths Chapter 7 Coordinate Geometry
• Two Dimensional Coordinate Geometry
• Coordinate Geometry Formulas

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NCERT Solutions for Class 10 Maths Chapter 7 Free PDF Download

Ncert solutions for class 10 maths chapter 7 – coordinate geometry.

NCERT Solutions for class 10 maths chapter 7 – Coordinate geometry will help you to make your foundation strong on the concepts of Coordinate geometry class 10. The study of Coordinate geometry class 10  and solving the problems will help you to solve complex problems easily. Coordinate geometry class 10 covers all the exercises provided in the NCERT textbook.

CBSE Class 10 Maths Chapter 7 NCERT Solutions are prepared by our expert at Toppr to help you to prepare for your exams in a better way and enhance your score. Coordinate geometry class 10  provide step by step solutions for the questions given in class 10 maths NCERT textbook as per CBSE Board guidelines and are also prepared according to the exam pattern. With the Toppr app, you can download NCERT Solutions for class 10 maths chapter 7 for free. In case you have a doubt while you are studying, Coordinate geometry class 10, for this we have a team of teachers who prove live doubt solving sessions only for you.

Download NCERT Solutions for Class 10 Maths Chapterwise here .

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CBSE Class 10 Maths Chapter 7 NCERT Solutions 

Coordinate geometry class 10 explains the distance between the two points whose coordinates, area of the triangle formed by three given points, coordinates of the point which divides a line segment joining two points in a given ratio, Distance formula, Section formula, Area of a Triangle. Also, the questions are solved with alternative solutions and diagrammatic representation.

Coordinate Geometry Sub-topics

• 7.1 – Introduction to Coordinate Geometry
• 7.2 – Distance Formula
• 7.3 – Section Formula
• 7.4 – Area of a Triangle
• 7.5 – Summary

You can download NCERT Solutions for Class 10 Maths Chapter 7 PDF for free by clicking on the button below.

NCERT Solutions for Class 10 Maths Chapter 7

Q.1 Find the distance between the following pairs of points: 

(2, 3), (4, 1) 

(−5, 7), (−1, 3) 

( a , b ), (− a , − b ) 

Distance between two points ( x 1 , y 1 ) and ( x 2 , y 2  ) is 

√ − ( x −−−−−−−−−−−−−−−− 1 − x 2 ) 2 + ( y 1 − y 2 ) − 2 (i) Distance between (2, 3) and (4, 1) 

= √ − (2 −−−−−−−−−−−−− − 4 ) 2 + (3 − 1 ) − 2 = √ − (−2 −−−−−−−− (2) 2 + ) − 2 = √ − 4+4 −−− = 8√ = 2 2√ 

(ii) Distance between (−5, 7) and (−1, 3) 

= √ − (−5 −−−−−−−−−−−−−−−−− − (−1) ) 2 + (7 − 3 ) − 2 = √ − (−4 −−−−−−−− (4) 2 + ) − 2 = √ − 16 −−−−− + 16 = √ −− 32= 4 2√ 

(iii )Distance between ( a , b ) and (− a , − b ) 

= √ − ( a − −−−−−−−−−−−−−−−−−− (− a ) ) 2 + ( b − (− b ) ) − 2 = √ − (2 a −−−−−−−− ) 2 + (2 b ) − 2 = √ − 4 −−−−−−− a 2 + 4 b 2 = 2 √ − a −−−−− 2 + b 2 #465323 Topic: Distance Between Two Points 

Q.2 Find the distance between the points (0, 0) and (36, 15) . 

Distance Between two given point= 

√ − ( x −−−−−−−−−−−−−−−− 2 − x 1 ) 2 + ( y 2 − y 1 ) − 2 Here 

x 1 = 0, x 2 = 26 and y 1 = 0, y 2 = 15 ∴ Distance between the points (0, 0) and (36, 15) = 

√ − (36 −−−−−−−−−−−−−− − 0 ) 2 + (15 − 0 ) − 2 = √ − +36 −−−−−−− 2 15 2 = √ − 1296 −−−−−−− + 225 − = √ − 1521 −−− = 39 

Q.3 Determine if the points (1, 5), (2, 3) and (−2, −11) are collinear. 

Three points A , B and C 

are collinear if 

AB + BC = AC 

Here, point A (1, 5), B (2, 3) and 

C (−2, −11). ∴ AB = √ − (2 −−−−−−−−−−−−− − 1 ) 2 + (3 − 5 ) − 2 = √ − 1 −−−−−−− 2 +(− 2 2 − ) = √ − 1+4 −−− = 5√ = 2.23 BC = √ − ((−2) −−−−−−−−−−−−−−−−−−−−−− − (2) ) 2 + ((−11) − (3) ) − 2 = √ − (−4 −−−−−−−−−− ) 2 + (−14 ) − 2 = √ − 16 −−−−−− + 196 = √ −−− 212 = 14.56 AC = √ − ((−2) −−−−−−−−−−−−−−−−−−−−−− − (1) ) 2 + ((−11) + (5) ) − 2 = ( √ − 3 ) 2 + (−16 ) 2 = √ − 9 −−−−− + 256 = √ −−− 265 = 16.27 AB + BC = 2.23 + 14.56 = 16.79 

AB + BC ≃ AC 

Hence the given points are collinear. 

Q. 4 Find the ratio in which the line segment joining the points (−3, 10) and (6, −8) is divided by (−1, 6) 

Let the required ratio be 

Take ( x 1 , y 1 ) = (−3, 10); ( x 2 , y 2 ) = (6, −8) and 

( x , y ) = (−1, 6) ∴ ⇒ x −1 = = m 1 xm m 2 1 1 + m 2 x 1 

m 2 ×−3 m 1 + m 2 ⇒− m 1 − m 2 =6 m − 3 m 2 

⇒− m 1 −6 m 1 =−3 m 2 + m 2 

⇒ −7 m 1 = −2 m 2 ⇒ m 1 m 2 

= 2 7 ∴ The required ratio is 2:7 

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• CBSE Class 10 Maths Chapter 7 - Coordinate Geometry Formula

Coordinate Geometry Formula for CBSE Class 10 Maths - Free PDF Download

Coordinate geometry is a very interesting branch of mathematics as it connects algebra and geometry by the use of graphs of lines and curves. The study of geometry using coordinate points is known as coordinate geometry. It primarily assists us in locating points in a plane. Its implementations can be found in a number of fields, including trigonometry, calculus, and dimensional geometry.

Coordinate geometry formulas Class 10 helps us to find the distance between two points, divide lines in m:n ratios, find the mid-point of a line, calculate the area of a triangle in the Cartesian plane. In this article, we will discuss all formulas of coordinate geometry class 10. Before studying formulas of coordinate geometry Class 10 students have to be familiar with basic concepts of coordinate geometry such as the representation of points on the cartesian coordinate system and the meaning of abscissa and ordinate.

Students can download the free PDF of coordinate geometry formula class 10 from the Vedantu website. This formula of coordinate geometry class 10 is prepared according to the NCERT curriculum. Experts in Vedantu have prepared this PDF of formulas after doing a lot of research on the Coordinate geometry chapter. The steps to derive the coordinate geometry formulas for class 10 are explained in a step-by-step manner by the experts so that students will have a good understanding of the concepts without any doubts. Vedantu is a platform that provides free CBSE Solutions and other study materials for students. You can Download Maths NCERT Solutions Class 10 to help you to revise the complete Syllabus and score more marks in your examinations. Subjects like Science, Maths, Engish will become easy to study if you have access to NCERT Solution for Class 10 Science , Maths solutions, and solutions of other subjects that are available on Vedantu only.

Coordinate Geometry Formulas Class 10

Here let us have a look at all formula of coordinate geometry Class 10.

Distance Formula

Section Formula

Area of a Triangle

A detailed explanation of coordinate geometry class 10 all formulas are given below.

Coordinate Geometry Class 10 Formulas - Distance Formula

To calculate the distance between two points the distance formula is used. Making a triangle by using the Pythagorean theorem to find the length of the hypotenuse gives the distance formula. The distance between the two points in a triangle is called the hypotenuse.

The distance formula can also be used to calculate the lengths of all the sides of a polygon, the perimeter of polygons on a coordinate plane, the area of polygons, and several other things.

The distance formula is denoted by ‘d’.

Distance Formula Between 2 Points in a 2D Plane:

Consider 2 points P and Q having the 2D coordinates as (x 1 ,y 1 ) and (x 2 ,y 2 ) respectively.

Now the distance between these 2 points in the 2D plane is

\[d = PQ = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}\]

Distance Formula Between 2 Points in a 2D Plane in Polar Coordinates:

Consider 2 points P and Q having the 2D polar coordinates as (r 1 ,θ 1 ) and (r 2 ,θ 2 ) respectively.

\[d = PQ = \sqrt{r_{1}^{2} + r_{2}^{2} - 2r_{1}r_{2} cos(\theta_{1} - \theta_{2})}\]

Distance Formula Between 2 Points in a 3D Plane:

Consider 2 points P and Q having the 3D coordinates as (x 1 ,y 1 ,z 1 ) and (x 2 ,y 2 ,z 2 ) respectively.

Now the distance between these 2 points in the 3D plane is

\[d = PQ = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} + (z_{2} - z_{1})^{2}}\]

Distance Formula Between a Point and a Line

Consider a straight line Ax + By + C = 0 and point P having the 2D coorrdinates as (x 1 , y 1 ).

Now the distance between the line Ax + By + C = 0 and a point P (x 1 , y 1 ) is

\[d = \frac{|Ax + By + C|}{\sqrt{A^{2} + B^{2}}}\]

Distance Formula Between Two Parallel Points

Consider two parallel lines y = mx + c 1 and y = mx + c 2 .

Now the distance between these two parallel lines is given by

\[d = \frac{|c_{1} - c_{2}|}{\sqrt{A^{2} + B^{2}}}\]

Problems on Distance formula

1. Find the distance between two points A and B which are having the 2D coordinates as (4, 8) and (3, 6) respectively.

Ans: The distance between these 2 points in the 2D plane is

\[d = AB = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}\]

Here x 1 = 4, x 2 = 8, y 1 = 3 and y 2 = 6. Now substituting these values in the distance formula we get,

\[d = AB = \sqrt{(8 - 4)^{2} + (6 - 3)^{2}}\]

\[d= AB = \sqrt{(4)^{2} + (3)^{2}}\]

\[d = AB = \sqrt{16 + 9}\]

\[d = AB = \sqrt{25}\]

d = AB = 5 units

So the distance between 2 points A and B is 5 units.

Coordinate Geometry Formulas Class 10 - Section Formula

The Section formula is used in coordinate geometry to find the ratio in which a line segment is separated by a point, either internally or externally. It is used to determine the triangle's centroid, incenter, and excenters.

Section Formula When the Line Segment Separated Internally by a Point

Consider a point P (x, y) dividing the line segment joining the points A(x 1 ,y 1 ) and B(x 2 ,y 2 ) internally in the ratio m:n.

Now the section formula for a line segment separated internally by a point is:

\[P(x, y) = (\frac{mx_{2} + nx_{1}}{m + n}, \frac{ny_{2} + ny_{1}}{m + n})\]

Section Formula When the Line Segment Separated Externally by a Point

Consider a point P (x, y) dividing the line segment joining the points A(x 1 , y 1 ) and B(x 2 , y 2 ) externally in the ratio m:n.

Now the section formula for a line segment separated externally by a point is:

\[P(x, y) = (\frac{mx_{2} - nx_{1}}{m - n}, \frac{ny_{2} - ny_{1}}{m - n})\]

Section Formula When Line Segment Separated Internally by a Point in the Ratio K:1

Consider a point P (x, y) dividing the line segment joining the points A(x 1 ,y 1 ) and B(x 2 ,y 2 ) internally in the ratio K:1.

\[P(x, y) = (\frac{Kx_{2} + x_{1}}{K + 1}, \frac{Ky_{2} + y_{1}}{K + 1})\]

Section Formula When Line Segment Separated Externally by a Point in the Ratio K:1

Consider a point P (x, y) dividing the line segment joining the points A(x 1 ,y 1 ) and B(x 2 ,y 2 ) externally in the ratio K:1.

\[P(x, y) = (\frac{Kx_{2} - x_{1}}{K - 1}, \frac{Ky_{2} - y_{1}}{K - 1})\]

Problems on Section Formula

1. Two points A (5,8) and B (3,6) on the line segment are separating the point P (x,y) internally in the ratio 2:4. By using the section formula find the ratio in which a line segment is separated by a point.

Ans: The section formula for a line segment separated internally by a point is given by the formula:

Here x 1 = 5, x 2 = 8, y 1 = 3 and y 2 = 6, m=2, n=4. Now substituting these values in the section formula we get,

\[P(x, y) = (\frac{(2 \times 8) + (4 \times 5)}{2 + 4}, \frac{(2 \times 6) + (4 \times 3)}{2 + 4})\]

\[P(x, y) = (\frac{16 + 20}{6}, \frac{12 + 12}{6}\]

\[P(x, y) = (\frac{36}{6}, \frac{24}{6})\]

P x, y = 6, 4

The ratio in which the line segment separated by a point internally is (6,4).

2. Two points A (5,8) and B (3,5) on the line segment are separating the point P (x,y) externally in the ratio 2:4. By using the section formula find the ratio in which a line segment is separated by a point.

Ans: the section formula for a line segment separated externally by a point is 

Here x 1 = 5, x 2 = 8, y 1 = 3 and y 2 = 5, m=2, n=4. Now substituting these values in the section formula we get,

\[P(x, y) = (\frac{(2 \times 8) - (4 \times 5)}{2 - 4}, \frac{(2 \times 5) - (4 \times 3)}{2 - 4})\]

\[P(x, y) = (\frac{16 - 20}{-2}, \frac{10 - 12}{-2}\]

\[P(x, y) = (\frac{-4}{-2}, \frac{-2}{-2})\]

P( x, y) = ( 2, 1)

The ratio in which the line segment separated by a point externally is (2, 1).

Formulas of Coordinate Geometry Class 10 - Area of a Triangle

The area of a triangle is defined as the total area enclosed by the triangle's three sides.

Here in this coordinate geometry all formula Class 10 we will discuss the area of the triangle of three different triangles namely right-angled triangle, equilateral triangle, and isosceles triangle.

Area of a Right Angled Triangle

A right-angled triangle is one in which one of the angles is the right angle. The hypotenuse is the hand opposite the right angle. Legs are the sides that are adjacent to the right angle.

The area of the right-angled triangle is:

A = ½ × Base × Height

Area of an Equilateral Triangle

An equilateral triangle is one in which all three sides are the same length and all three internal angles are congruent and 60°each.

The area of an equilateral triangle is:

\[A = \frac{\sqrt{3} \times a^{2}}{4}\]

Area of an Isosceles Triangle

A triangle with two sides of equal length is called an isosceles triangle.

The area of an isosceles triangle is:

Area of Triangle With all 3 Sides Different

When all 3 sides of a triangle are different, then to find the area of the triangle we will use Heron’s formula.

When the lengths of all three sides are known, Heron's formula, named after Hero of Alexandria, measures the area of a triangle. Unlike other triangle area formulas, no angles or other distances in the triangle must be determined first.

Heron’s formula to calculate the area of the triangle is:

\[A = \sqrt{s(s - a)(s - b)(s - c)}\]

Where ‘s’ is the semi perimeter of the triangle and a, b and c are the sides of the triangle.

Semi perimeter of the triangle is given by:

S = (a + b + c)/2

Problems on Area of Triangle

1. If the base of the right-angled triangle is 4 cm and height is 6 cm. Find the area of the triangle.

Ans: The area of the right-angled triangle is:

Here Base = 4 cm and Height = 6 cm. Substituting these values in the formula we get,

A = ½ × 4 × 6

A = 12 cm 2.

Therefore the area of the right-angled triangle is 12 cm 2 .

2. If the three sides of a triangle are having the same length equal to 6 cm. Find the area of the triangle and name the type of triangle.

Ans: If all three sides are the same length then the triangle is an equilateral triangle.

Here ‘a’ is the sides of the triangle given as 6cm. So substituting this value we get 

\[A = \frac{\sqrt{3} \times 6^{2}}{4}\]

\[A = \frac{\sqrt{3} \times 36}{4}\]

\[A = \sqrt{3} \times 9\]

\[A = 9\sqrt{3}\] cm 2

Therefore the area of the equilateral triangle is \[9\sqrt{3}\] cm 2 .

One of the most important and exciting concepts in mathematics is coordinate geometry. By the use of graphs of lines and curves, it connects algebra and geometry. This allows algebraic solutions to geometric problems and offers geometric insights into algebra. These coordinate geometry Class 10 formulas will help students to understand the basic concepts of geometrical structures and to apply them in our daily uses too.

FAQs on CBSE Class 10 Maths Chapter 7 - Coordinate Geometry Formula

1. What are the Important Coordinate Geometry Formulas Class 10?

Ans: There are three important formulas in coordinate geometry studied in Class 10.

2. What is the Distance Formula? Write the Distance Formula Between Two Points in a 2D Plane.

Ans: Distance formula is used to distance between two points in a 2D or a 3D plane. Also, it is used to calculate the distance between a point and a line, the distance between two parallel points.

The distance formula between two points in a 2D plane is 

d = PQ = √[(x 2 - x 1 ) 2 + (y 2 - y 1 ) 2 ]

3. What is the Section Formula? Write the Section Formula when the Line Segment is Separated by Point Internally and Externally?

Ans: The Section formula is used in coordinate geometry to find the ratio in which a line segment is separated by a point, either internally or externally. It is used to determine the triangle's centroid, incenter, and excenters.

Section formula for a line segment separated internally by a point is 

P x,y = [ (mx 2 + nx 1 )/ (m + n) , (my 2 + ny 1 )/ (m + n) ]

The section formula for a line segment separated externally by a point is 

P x,y = [ (mx 2 - nx 1 )/ (m - n) , (my 2 - ny 1 )/ (m - n) ]

Chapterwise CBSE Class 10 Maths Formula

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NCERT Solutions for Class 10 Maths Ch 7 Coordinate Geometry

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry

• Exercise 7.1
• Exercise 7.2
• Exercise 7.3
• Exercise 7.4

How many exercises in Chapter 7 Coordinate Geometry

What is coordinate geometry, find the point on y-axis which is equidistant from the points (5, − 2) and (− 3, 2)., if the points a (4, 3) and b (x, 5) are on the circle with the centre o (2, 3), find the value of x., contact form.

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CBSE 10th Standard Maths Subject Case Study Questions with Solutions

By QB365 on 20 May, 2021

QB365 Provides the updated CASE Study Questions for Class 10 , and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get  more marks in Exams

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