case study on coordinate geometry class 8

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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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CBSE Class 10 Maths Best Study Material for 2021-2022

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CBSE 8th Standard CBSE all question papers, important notes , study materials , Previuous Year questions, Syllabus and exam patterns. Free 8th Standard CBSE all books and syllabus online. Practice Online test for free in QB365 Study Material. Important keywords, Case Study Questions and Solutions. Updates about latest education news and Scholorships in one place.

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• Coordinate Geometry

Do you remember what a plane is? A plane is any flat surface which can go on infinitely in both of the directions. Now, if there is a point on a plane , you can easily locate that point with the help of coordinate geometry. Using the two numbers of the coordinate geometry, a location of any point on the plane can be found. Let us know more!

A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates .

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What are Coordinates?

Now, to help you understand the coordinates, take a look at the figure below.

Now, consider the grid on the right. The columns of the grid are labeled as A, B, C, D, E, F, etc. On the other hand, the rows are numbered as 1, 2, 3, 4, 5, 6, and so on. You can see that the letter X is located in the box D3 i.e. column D and row 3.  Here, D and 3 are the coordinates of this box.

The box has two parts – one is the row and the other is the column. You need to understand that there are several boxes in every row and several boxes in every column. So, when you have both of them, you can find one single box that is the point where the rows and the columns intersect each other.

Download Coordinate Geometry Cheat Sheet Below

Browse more Topics Under Coordinate Geometry

• Areas of Triangles and Quadrilaterals
• Distance Formula
• Section Formula

The Coordinate Plane

In the coordinate geometry, all the points are located on the coordinate plane. Take a look at the figure below.

The figure above has two scales – One is the X-axis which is running across the plane and the other one is the y-axis which is at the right angles to the X-axis. This is similar to the concept of the rows and columns that we discussed in the first part above.

Understanding the Concept of Coordinates

• The point of intersection of the x and the y-axis is known as the origin . At this point, both x and y are 0.
• The values on the right-hand side of the x-axis are positive and the values on the left-hand side of the x-axis are negative.
• Similarly, on the y-axis, the values located above the origin are positive and the values located below the origin are negative.
• When you have to locate a point on the plane, it is determined by a set of two numbers . So, first, you have to write about its location on the x-axis followed by its location on the y-axis. Together, the two will determine a single and unique position on the plane.

So, in the figure above, the point A has a value 20 on the x-axis and value 15 on the y-axis. These are also the coordinates of the point A. Often these points are also regarded as the “rectangular coordinates”. Please note: The order of the points on the plane is crucial. You have to write the x coordinate ahead of the y coordinate.

Things That Have Been Made Possible By Coordinate Geometry

If you know the coordinates of a group of points, you can do the following:

• Determine the distance between these points.
• Find the equation , midpoint, and slope of the line segment.
• Determine if the given lines are perpendicular or parallel.
• Find the perimeter and the area of the polygon formed by the points on the plane.
• Transform the shape by reflecting, moving and rotating it.
• Define the equations of ellipses , curves , and circles .

Question For You

Question 1: What is the name of horizontal and vertical lines that are drawn to find out the position of any point in the Cartesian plane?

Answer : The name of horizontal and vertical lines that are drawn to find out the position of any point in the Cartesian plane are determined by x-axis and y-axis respectively.

Question 2: Who is the father of coordinate geometry?

Answer:   The father of coordinate geometry was René Descartes. He was referred to as the father of analytical geometry due to his contributions to the field. As his Latin name was Renatius Cartesius, thus we learn that the terms ‘Cartesian plane’ and ‘Cartesian coordinate system’ were a derivative of this man’s name.

Question 3: What do we need to coordinate geometry for?

Answer: Coordinate geometry is needed to offer a connection between algebra and geometry with the use of graphs of lines and curves. It is an essential branch of math and usually assists us in locating points in a plane. Moreover, it also has many uses in fields of trigonometry, calculus, dimensional geometry and more.

Question 4: What is Section Formula?

Answer: Section formula helps us knowing the coordinates of the points that are dividing a given line segment into two parts. This allows the lengths to be in the ratio m: n m: n m: n. Thus, the midpoint of a line segment is the point which divides a line segment into two equal halves.

Question 5: What is the definition of coordinate geometry in math?

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• RS Aggarwal Solutions Class 8 Chapter-22 Introduction to Coordinate Geometry (Ex 22A) Exercise 22.1
• RS Aggarwal Solutions

RS Aggarwal Solutions Class 8 Chapter-22 Introduction to Coordinate Geometry (Ex 22A) Exercise 22.1 - Free PDF

Free PDF download of RS Aggarwal Solutions Class 8 Chapter-22 Introduction to Coordinate Geometry (Ex 22A) Exercise 22.1 solved by Expert Mathematics Teachers on Vedantu.com. All Exercise 22.1 Questions with Solutions for Class 8 RS Aggarwal to help you to revise complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other Engineering entrance Exams.

Register Online for Class 8 Science tuition on Vedantu.com to score more marks in CBSE board Examination . Vedantu is a platform that provides free CBSE Solutions (NCERT) and other study materials for students. Maths Students who are looking for the better solutions, can download Class 8 Maths NCERT Solutions to help you to revise the complete syllabus and score more marks in your Examinations.

Class 8 Chapter-22 Introduction to Coordinate Geometry

Geometry is a branch of Mathematics that is related to the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs. It is mainly concerned with properties related to distance, shape, size, and relative position of figures. Applications of Geometry in the real world will enlighten you in areas that include computer-aided design for construction blueprints, the design of assembly systems in manufacturing, nanotechnology, computer graphics, visual graphs, video game programming, and virtual reality creation.

Geometry is also used in many scientific and technical areas, such as mechanics, astronomy, crystallography, engineering, architecture, geodesy, aerodynamics, and navigation.  Geometry is easily present everywhere in nature, as we discover more and more about our environment and our surroundings we see so many simple Examples such as spheres, triangles, squares, lines, etc.  

Various Ways on How Geometry is Used in Everyday Activity in Our Lives

The major use of Geometry is in the construction field. They are used for designing plans for building dams, temples, roads, homes, monuments, etc.

It is very helpful in the science industry in scientific research methods and also in measuring orbits and planetary motions.

Geometry allows you to determine and figure out how shapes and figures fit together to maximize efficiency and visual appeal in real life .

Geometry is used for computer imaging, designing, creating video games, animations, and things like that are made using geometric concepts. 

 Some important professions like the medical industry benefit from geometric imaging. Technologies such as MRIs and CT scans are most efficiently used both for surgical aids and diagnosis.

A Mathematician usually applies Mathematical techniques and theories to real-life problems to effectively solve them in a proper method. Their main duties include gathering and analyzing research data, resolving challenges in other sectors like government, science, engineering, and business, uncovering and finding unknown relationships between various Mathematical principles, and using models to resolve problems and present solutions to necessary leadership teams.

Lots of young budding Game developers or video game developers, create video games for various systems, design mobile applications, computers, and consoles. Their other major responsibilities include coding the bases for the games, troubleshooting and testing designs to fix any major issues, and assisting in the development of characters, levels, or storylines further.

FAQs on RS Aggarwal Solutions Class 8 Chapter-22 Introduction to Coordinate Geometry (Ex 22A) Exercise 22.1

1. Is Geometry a good scoring subject?

Maintain a separate revision note for writing formulas, theories, or methods used for any specific problems you find difficult or important. Understand the syllabus really well, try working out all problems yourself and practice well. Vedantu provides you with lots of sample question papers and past year question papers with which you can practice before Exams and that will help you in scoring well.

2. How to prepare for Exams efficiently in a short period?

Refer to past year’s question papers and sample question papers and work out every problem. Vedantu provides questions with solutions curated by experts for you to practice. This will also help you manage time and plan accordingly before the actual Exams. Practice writing, drawing, and presenting your paper neat so that you can score well.

3. How to find important questions that appear often in Exams?

If you search and collect past year question papers and find the often repetitive questions that appear in all papers. Note down those questions separately and work out with extra effort and practice well. Spending some extra time in your Mathematics subject will help you score well and as a result, helps in boosting your overall percentage. 

4. Why is it so nervous for students before examinations?

Students face so much pressure to score well like societal pressure, family pressure, and other unnecessary comparisons around them. This will build lots of tension and because of this students even if they have prepared well will likely have chances to forget the answers or even write wrong answers they already know well. This is unwanted tension built in their mind before Exams. So parents should make all arrangements to see if they are relaxed and well prepared without any tension.

5. Is it really necessary to score well in higher secondary grades?

Yes absolutely it is necessary to score well in higher secondary grades. These scores will help you to decide what career awaits you in your future. In order to build a strong base in academics and choose which institution you would like to get into with good grades, these scores are really necessary. You cannot get into well-reputed colleges that will provide decent placement offers.

Class 8 Maths Chapter 7 Previous Year Questions - Coordinate Geometry

Q2:  Assertion (A): Point P(0, 2) is t be point of intersection of y-axis with the line 3x + 2y = 4. Reason (R): The distance of paint P(0, 2) from x-axis is 2 units. (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (c) Assertion (A) is true, but Reason (R) is false. (d) Assertion (A) is false but Reason (R) is true.    [2023, 1 Mark] Ans:  (b) Point P(0, 2) is the point of intersection of y-axis with line 3x + 2y = 4

Also, the distance of point P(0, 2) from x-axis is 2 units.

Q3: The distance of the point (-6, 8) from origin is (a) 6 (b) -6 (c) 8 (d) 10    [2023, 1 Mark] Ans:  (d) Distance of the point (-6, 8) from origin (0, 0)

Q4: The points (-4, 0), (4, 0) and (0, 3) are the vertices of a (a) right triangle (b) isosceles triangle (c) equilateral triangle (d) scalene triangle    [2023, 1 Mark] Ans: (b) The points be A(-4, 0), B(4, 0) and C(0, 3). Using distance formula

Q5: The centre of a circle is (2a, a - 7). Find the values of 'a' if the circle passes through the point (11, -9). Radius of the circle is 5√2 cm.      [2023, 3 Marks] Ans:  Given centre of a circle is(2a, a - 7 )

Using section formula, we have

Hence, the required ratio is 2 : 1.

Q7: Case Study:  Jagdish has a Field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables (as shown in the figure). In the field, there is a pole marked as O.      [2023, 4,5,6 Marks]

Based on the above information, answer the following questions: (i)  Taking O as origin, coordinates of P are (-200, 0) and of Q are (200, 0). PQRS being a square, what are the coordinates of R and S? (ii) (a) What is the area of square PQRS?

(b) What is the length of diagonal PR in square PQRS? (iii) If S divides CA in the ratio K: 1, what is the value of K, where point A is (200, 800)? Ans: (i) We have. P = (-200, 0) and Q- = (200, 0)

The coordinates of R and S are (200, 400) and (-200, 400). (ii) (a)  The length PQ = 200 + 200 = 400 units. Area of square PQRS = 400  x 400 = 160000 sq. units.

Q2: The point on x-axis equidistant from the points P(5, 0) and Q(-1, 0) is (a) (2, 0) (b) (-2, 0) (c) (3, 0) (d) (2, 2)     [2022, 1 Mark] Ans:  (a) Let coordinates of the point on the x-axis be R (x, 0). Given, PR = QR ⇒ PR 2 = QR 2    ⇒ (x - 5) 2 + (0 - 0) 2 = (x + 1) 2 + (0 - 0) 2   ⇒ x 2  - 10x + 25 = x 2 + 2x + 1 ⇒ 12x =24 ⇒ x = 2 Required point is (2, 0).

Q3: The x-coordinate of a point P is twice its y-coordinate. If P is equidistant front Q(2, -5) and R(-3, 6), then the coordinates of P are (a) (8, 16) (b) (10, 20) (c) (20, 10) (d) (16, 8)     [2022, 1 Mark] Ans: (d) Let coordinate of point P= t So, .(x-coordinate of point P = 2t  ∴ Point is P (2t, t). Given, PQ = RP ⇒ PQ 2 = RP 2   ⇒ (2t - 2) 2 + (t + 5) 2 = (2t + 3) 2 + (t - 6) 2   [By distance formula] ⇒ 4t 2  - 8t + 4 + t 2 + 10t + 25 = 4t 2 + 12t + 9  +  t 2 - 12t + 36 ⇒ 2t = 16 t = 8 Coordinates of P are (16,  8).

Based on the above information, answer the following questions: Q5: If O is the origin, then what are the coordinates of S? (a) (-6, -4) ( b) (6, 4) (c) (-6, 4) ( d) (6, -4)      [2022, 1 Mark] Ans: (c) Coordinates of S are (-6, 4).

Q9: The coordinates of the vertices of rectangle IJKL are (a) I(2, 0), J(2, 6), K(8,6), L(8, 2) (b) I(2, -2), J(2, -6), K(8, - 6), L(8, -2) (c) I(-2, 0), J(-2, 6), K(-8, 6), L(-8, 2) (d) I(-2, 0), J(-2, -6), K(-8, -6), L(-8, -2)      [2022, 1 Mark] Ans: (b) Coordinates of vertices of rectangle IJKL are respectively I(2, -2), J(2, -6), K(8, -6),L(8, -2).

Q1: Case Study :  Students of a school are standing in rows and columns in their school playground to celebrate their annual sports day. A, B, C and D are the positions of four students as shown in the figure.

∴ OA is the minimum distance ∴ A is closest to sports teacher.

Since. AB = BC ∴ ABC is an isosceles triangle. Also, AB 2 + BC 2 = 106 + 106 = 212 = AC 2 So. ABC is an isosceles right angled triangle with ∠B = 90°.

Q5: The point on the x-axis which is equidistant from (-4, 0) and (10, 0) is (a) (7, 0) (b) (5, 0) (c) (0, 0) (d) (3, 0)        [2020, 1 Mark] Ans: (d) Let coordinates of the point on the x-axis be P(x, 0). Let the given points be A(-4, 0) and B(10, 0). which also lie on x-axis. Since P is equidistant from A and B. ∴ x = -4 + 10 / 2 = 6 / 2 = 3 So, P(3, 0) is equidistant from A(-4, 0) and B(10, 0).

Q6: If the point P(k, 0) divides the line segment joining the points A(2, -2) and B(-7, 4) in the ratio 1:2 then the value of k is (a) 1 (b) 2 (c) -2 (d) -1      [2020, 1 Mark] Ans: (d) Since, the point P(k 0) divides the line segment joining A(2, -2) and B(-7, 4) in the ratio 1 : 2.

Q2: Find the point on y-axis which is equidistant from the points (5,-2) and (-3, 2).        [Delhi 2019, 3 Marks] Ans: Let P(0, y) be the point on the y-axis which is equidistant from A(5, - 2) and B(-3, 2).

AP = BP ⇒ (AP) 2  = (BP) 2 ⇒ (5 - 0) 2 + (-2 - y) 2 = (-3 - 0) 2  + (2 - y) 2 ⇒ 25 + 4 + y 2 + 4y = 9 + 4 + y 2 - 4y ⇒ 8y = 9 - 25 ⇒ y = -16/2 = -2 Hence, A and B are equidistant from (0, -2).

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Eighth Grade (Grade 8) Coordinate Geometry Questions

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Practice Questions on Coordinate Geometry

In this article, we will learn about one interesting topic which is covered in class 9 and class 10 mathematics. We will look at some formulas and problems of Coordinate Geometry .

Important Formulas

General Form of a Line : Ax + By + C = 0 Slope Intercept Form of a Line : y = mx + c Point-Slope Form : y − y1= m(x − x1) The slope of a Line Using Coordinates : m = Δy/Δx = (y2 − y1)/(x2 − x1) The slope of a Line Using General Equation : m = −(A/B) Intercept-Intercept Form : x/a + y/b = 1 Distance Formula : |P1P2| = √[(x2 − x1) 2 + (y2 − y1) 2 ] For Parallel Lines : m1 = m2 For Perpendicular Lines : m1m2 = -1 Midpoint Formula : M (x, y) = [½(x1 + x2), ½(y1 + y2)] Angle Formula : tan θ = [(m1 – m2)/ (1 + m1m2)] Area of a Triangle Formula = ½ |x1(y2−y3)+x2(y3–y1)+x3(y1–y2)| Distance from a Point to a Line : d = [|Ax 0 + By 0 + C| / √(A 2 + B 2 )]

Practice Problems with Solutions:

Q1. find the equation of a line which passes through the points (3, 4) and (5, 8) in the general form..

To find the equation of a line in the general form, follow these steps: Step 1: Find the slope (m): m= (8-4)/(5-3) m = 2 Step 2: Use the point slope form through (3, 4) y – 4 = 2(x – 3) y – 4 = 2x – 6 y = 2x – 2 Step 3: Now, convert to the general form 2x – y – 2 =0

Q2. Find the equation of a line passing through the point (2, 3) with slope 2 in slope-intercept form y=mx+c.

The point-slope form equation of line is y – y1 = m(x – x1) Given point = (2, 3) slope = m =2 Now, y – 3 = 2(x – 2) y – 3 = 2x – 4 y = 2x – 1 So, the equation of a line passing through the point (2, 3) with slope 2 is y = 2x – 1.

Q3. Find the slope of the line passing through the points (2, 5) and (6, 9).

To find the slope of the line passing through the points (2, 5) and (6, 9), use the following formula m = (y2 – y1)/(x2 – x1) m = (9 – 5)/(6 – 2) m = 1. So, the slope of the line passing through the points (2, 5) and (6, 9) is 1.

Q4. Find the equation of a line with x-intercept 4 and y-intercept 5 in intercept-intercept form x/a+y/b=1.

Given, x-intercept = 4 y- intercept = 5 equation of line = x/a + y/b = 1. x/4 + y/5 = 1 5x + 4y = 20. So, the equation of a line with x-intercept and y-intercept is 5x + 4y = 20.

Q5. Find the distance between the points (2, 3) and (5, 7) using the distance formula.

The distance formula is d = √[(x2 − x1) 2 + (y2 − y1) 2 ] Given points are (2, 3) and (5, 7). Now, d = √[(5 – 2) 2 + (7 – 3) 2 d = √(3) 2 + (4) 2 d = √9 + 16 d = √25 d = 5 So, the distance between the points (2, 3) and (5, 7) is 5.

Q6. Determine if the lines with equations 2x+3y−5=0 and 4x+6y−10=0 are parallel.

To check whether the given pair of lines are parallel, we need to check their slope if m1 = m2, then they are parallel. Now, to calculate slope of first line 2x + 3y -5 = 0 m1 = -(a/b) m1 = -2/3 Now, we calculate slope of second line 4x + 6y – 10 = 0 m2 = -(a/b) m2 = -(4/6) m2 = -2/3 Here, m1 = m2 So, the lines 2x + 3y – 5 = 0 and 4x + 6y – 10 = 0 are parallel lines.

Q7. Determine if the lines with equations 3x+4y−7=0 and 4x−3y−5=0.

To check whether the given pair of lines are perpendicular, we need to check their slope if m1.m2 = -1, then they are perpendicular. Now, to calculate slope of first line 3x + 4y – 7 = 0 m1 = -(a/b) m1 = -3/4 Now, we calculate slope of second line 4x – 3y – 5 = 0 m2 = -(a/b) m2 = -(4/-3) m2 = 4/3 now, m1.m2 = (-3/4).(4/3) = -1 So, the lines 2x + 3y – 5 = 0 and 4x + 6y – 10 = 0 are perpendicular lines .

Q8. Find the midpoint of the line segment with endpoints (1, 2) and (5, 8).

to find the midpoint use the following formula M(x, y) = [(x1 + x2)/2, (y1 + y2)/2] now, M(x, y) = [(1+5)/2, (2+8)/2] M(x, y) = [6/2, 10/2] M(x, y) = (3, 5) Hence, the middle point is (3, 5).

Q9. Find the area of the triangle formed by the vertices (4, 5), (10, 12) and (-3, 2).

To find the area use the following formula Area = ½ |x1(y2−y3)+x2(y3–y1)+x3(y1–y2)| so, area of triangle = x1y2 – x1y3 + x2y3 – x2y1 + x3y1 – x3y2 area of triangle = 1/2 [4×12 – 4×2 + 10×2 – 10×(5) + (-3)×5 – (-3)×12] area of triangle = 1/2[48 – 8 + 20 – 50 – 15 + 36] area of triangle = 1/2[71] area of triangle = 71/2 So, the area of triangle is 71/2.

Q10. Find the distance from the point (2, 5) to the line 3x+4y−12=0.

To find the distance from a point to the line , use this formula d = [|Ax0 + By0 + C| / √(A 2 + B 2 )] Now, given line = (Ax + By + C = 0) = 3x + 4y -12 = 0 so, A = 3, B = 4 and C = -12 given point = (x0, y0) = (2, 5) So, x0 = 2, y0 = 5 d = [|Ax0 + By0 + C| / √(A2 + B2)] d = [|3 × 2 + 4 × 5 – 12| / √(3 2 + 4 2 )] d = [|6 + 20 – 12| / √(9 + 16)] d = [|14| / √(25)] d = 14/5 So, the distance from a point (2, 5) to the line (3x + 4y – 12 = 0) is 14/5

Unsolved questions

Q1. Find the equation of a line passing through the points (-1, 3) and (2, -5) in the general form Ax+By+C=0.

Q2. Find the equation of a line passing through the point (3, -2) with slope -1 in slope-intercept form y=mx+c.

Q3. Find the equation of the line passing through the point (-4, 6) with slope 4 in point-slope form 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1).

Q4. Find the slope of the line passing through the points (-3, 5) and (7, 2).

Q5. Find the slope of the line represented by the equation 2x−3y+6=0.

Q6. Find the equation of a line with x-intercept 3 and y-intercept -4 in intercept-intercept form x/a+y/b=1.

Q7. Determine if the lines with equations 4x+2y−8=0 and 8x+4y−16=0 are parallel.

Q8. Determine if the lines with equations 5x+2y−10=0 and 2x−5y+15=0 are perpendicular.

Q9. Find the distance between the points (-2, 4) and (6, -1) using the distance formula.

Q10. Find the midpoint of the line segment with endpoints (-3, 7) and (5, -4).

Related Articles:

FAQs on Coordinate Geometry

What are coordinate geometry.

Coordinate geometry is a system in which we makes use of the coordinate points to study the geometry. It is also used to describe the link between the geometry and the algebra.

Find the slope of the line 4x – 6y = 12

To find the slope of the line 4x – 6y = 12, slope = -(4/(-6)) slope = 2/3

What methods can be used to solve coordinate geometry?

To solve coordinate geometry, we can use formulas like stance formula, slope formula, midpoint formula, the equation of a line, etc .

What does it mean when two pair of lines are parallel?

When two pair of lines are parallel, that means their slopes are equal

What does it mean when two pair of lines are perpendicular?

When two pair of lines are perpendicular, that means the product of the slopes is = -1.

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Case Study Questions for Class 8 Maths Chapter 4 Practical Geometry

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Here we are providing Case Study questions for Class 8 Maths Chapter 4 Practical Geometry .

Practical Geometry Class 8 Maths Case Study Questions

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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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Class 9 Maths Case Study Questions Chapter 3 Coordinate Geometry

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Case study Questions in Class 9 Mathematics Chapter 3  are very important to solve for your exam. Class 9 Maths Chapter 3 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving  Class 9 Maths Case Study Questions  Chapter 3 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 9 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 9 Maths Chapter 3 Coordinate Geometry

Case Study/Passage-Based Questions

Answer: (d) 2 units

(ii) How far is the library from Shaguns house?

Answer: (b) 2 units

(iii) How far is the library from Alia’s house?

Answer: (d) None of these

(iv) Which of the following is true?

Answer: (b) ABC forms an isosceles triangle

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 house from grocery store to that from electrician’s shop, is

Answer: (c) 1.2

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

Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Mathematics Chapter 3 Coordinate Geometry with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 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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• CBSE Maths Important Questions
• Class 8 Maths
• Chapter 15: Introduction to Graphs

Important Questions Class 8 Maths Chapter 15: Introduction to Graphs

Important questions with solutions for Class 8 Maths Chapter 15 (Introduction to Graphs) has been provided here by our subject experts. The extra questions are available here to help students score better marks in final exam 2022 – 2023 . The materials provided at BYJU’S for CBSE students are as per the latest syllabus and in reference with NCERT book .

In this chapter, students will go through plotting the graph for the different given situations. For example, change in temperature with respect to the number of days can be plotted in an XY plane. The problems and solutions for graphs will consist of such scenarios. To prepare for Maths exam practice Class 8 Maths Important questions for all the chapters here.

Also Check:

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Important Questions With Solutions For Maths Class 8 Chapter 15 (Introduction to Graphs)

Q.1: The following line graph shows the yearly sales figures for a manufacturing company.

(a) What were the sales in (i) 2002 (ii) 2006?

(b) What were the sales in (i) 2003 (ii) 2005?

(c) Compute the difference between sales in 2002 and 2006.

(d) In which year was there the greatest difference between the sales as compared to its previous year?

(a) The sales in (i) 2002 were Rs. 4 crores and (ii) 2006 was Rs. 8 crores

(b) The sales in (i) 2003 was Rs. 7 crores and (ii) 2005 was Rs.10 crores.

(c) The difference of sales in 2002 and 2006 = Rs. 8 crores – Rs. 4 crores = Rs. 4 crores

(d) In the year 2005, there was the greatest difference between the sales and compared to its previous year, which is (Rs. 10 crores – Rs. 6 crores) = Rs. 4 crores.

Q.2: Use the tables below to draw linear graphs:

(a) The number of days a hillside city received snow in different years.

(b)Population (in thousands) of men and women in a village in different years.

a) Consider “Years” along the x-axis and “Days” along the y-axis. Using the given information, the linear graph will look like:

b) Consider “Years” along the x-axis and “No. of Men and No. of Women” along the y-axis (2 graphs). Using the given information, the linear graph will look like:

Q.3: Plot the point (4, 3) on a graph sheet. Is it the same as the point (3, 4)?

Locate the x, y axes, (they are actually number lines!). Start at O (0, 0). Move 4 units to the right; then move 3 units up, you reach the point (4, 3). From Fig 15.13, you can see that the points (3, 4) and (4, 3) are two different points.

Q.4: Plot the following points on a graph sheet. Verify if they lie on a line:

(a) A(4,0), B(4, 2),C(4,6), D(4, 2.5)

(b) P(1, 1), Q(2, 2), R(3,3), S(4, 4)

(c) K(2, 3), L(5, 3), M(5,5), N(2, 5)

Plot all the points on the graph.

(a) All points A, B, C and D lie on a vertical line.

(b) P, Q, R and S points also make a line. It verifies that these points lie on a line.

(c) Points K, L, M and N do not lie in a straight line

Q.5: Draw the line passing through (2,3) and (3,2). Find the coordinates of the points at which this line meets the x-axis and y-axis.

Graph for the Line passes through points (2, 3) and (3, 2) is:

The coordinates of the points at which this line meets the x-axis at (5, 0) and Y axis at (0, 5).

Q.6: Draw the graphs for the following table of values, with suitable scales on the axes.

Interest on deposits for a year.

(i) Does the graph pass through the origin?

(ii) Use the graph to find the interest on Rs 2500 for a year.

(iii) To get an interest of Rs. 280 per year, how much money should be deposited?

Represent “Deposit” on y-axis and “simple interest” on x-axis.

(i) Yes, the graph passes through the origin.

(ii) Interest on Rs. 2500 is Rs. 200 for a year.

(iii) Rs. 3500 should be deposited for the interest of Rs. 280

Extra Questions For Class 8 Maths Chapter 15

• Plot the following points and verify if they lie on a line. If they lie on a line, name it.

(i) (0, 2), (0, 5), (0, 6), (0, 3.5)

(ii) A (1, 1), B (1, 2), C (1, 3), D (1, 4)

(iii) K (1, 3), L (2, 3), M (3, 3), N (4, 3)

(iv) W (2, 6), X (3, 5), Y (5, 3), Z (6, 2)

• State whether True or False. Correct that is false.

(i) A point whose x coordinate is zero and y-coordinate is non-zero will lie on the y-axis.

(ii) A point whose y coordinate is zero and x-coordinate is 5 will lie on y-axis.

(iii) The coordinates of the origin are (0, 0)

• A bank gives 10% Simple Interest (S.I.) on deposits by senior citizens. Draw a graph to illustrate the relation between the sum deposited and simple interest earned. Find from your graph

(a) the annual interest obtainable for an investment of ` 250.

(b) the investment one has to make to get an annual simple interest of ` 70.

• Draw a graph for the following.

Is it a linear graph?

5. Write the coordinates of each point shown is the graph.

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CBSE Class 8th Maths Value Based Questions Chapter 15 Introduction to Graphs PDF Download

CBSE Class 8th Maths Value Based Questions Chapter 15 Introduction to Graphs are the easiest questions which you see in your question paper and the scoring one all student who attempt it surely get they are just little bit difficult and examine your basic knowledge regarding the particular chapter. Maths Value Based Questions for Class 8th are available here at Free of cost. These questions are expected to be asked in the Class 8th board examination. These Maths Value Based Questions are from complete CBSE Syllabus.

CBSE Class 8th Maths Value Based Questions Chapter 15 Introduction to Graphs

Most of these Maths Value Based Questions are quite easy and students need only a basic knowledge of the chapter to answer these questions. Download CBSE Maths Value Based Questions for board examinations. These Maths Value Based Questions are prepared by Directorate of Education, Delhi.

CBSE Maths Value Based Questions Class 8th Chapter 15 Introduction to Graphs PDF

The purpose of the Maths Value Based Questions is to make students aware of how basic values are needed in the analysis of different situations and how students require to recognize those values in their daily lives. Some questions are subject related. But even if they are not, that one-minute awareness of what we write about value without any specific preparation is a good step indeed.

CBSE Maths Value Based Questions for Class 8th Chapter 15 Introduction to Graphs download here in PDF format. The most CBSE Maths Value Based Questions for annual examination are given here for free of cost. The additional questions for practice the Class 8th exam are collected from various sources. It covers questions asked in previous year examinations.

CBSE Maths Value Based Questions for Class 8th Chapter 15 Introduction to Graphs Free PDF

Class 8th books have many questions. These questions are regularly asked in exams in one or other way. Practising such most CBSE Maths Value Based Questions Chapter 15 Introduction to Graphs certainly help students to obtain good marks in the examinations. 

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CBSE Case Study Questions for Class 9 Maths Coordinate Geometry Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 9 Maths Coordinate Geometry  in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

CBSE Case Study Questions for Class 9 Maths Coordinate Geometry PDF

Checkout our case study questions for other chapters.

• Chapter 1 Number Systems Case Study Questions
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Solve every question of NCERT by hand, without looking at the solution.

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Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

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