case study co ordinate geometry

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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

Also Check:

Tips to Solve Case Study Based Questions Accurately

CBSE Class 10 Maths Best Study Material for 2021-2022

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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

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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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• Math Article
• Coordinate Geometry

Co-ordinate Geometry

Coordinate Geometry is considered to be one of the most interesting concepts of mathematics. Coordinate Geometry (or the analytic geometry ) describes the link between geometry and algebra through graphs involving curves and lines. It provides geometric aspects in Algebra and enables them to solve geometric problems. It is a part of geometry where the position of points on the plane is described using an ordered pair of numbers. Here, the concepts of coordinate geometry (also known as Cartesian geometry) are explained along with its formulas and their derivations.

Introduction to Coordinate Geometry

Coordinate geometry (or analytic geometry) is defined as the study of geometry using the coordinate points. Using coordinate geometry, it is possible to find the distance between two points, dividing lines in m:n ratio, finding the mid-point of a line, calculating the area of a triangle in the Cartesian plane, etc. There are certain terms in Cartesian geometry that should be properly understood. These terms include:

What is a Co-ordinate and a Co-ordinate Plane?

You must be familiar with plotting graphs on a plane, from the tables of numbers for both linear and non-linear equations. The number line which is also known as a Cartesian plane is divided into four quadrants by two axes perpendicular to each other, labelled as the x-axis ( horizontal line ) and the y-axis( vertical line ).

The four quadrants along with their respective values are represented in the graph below-

• Quadrant 1 : (+x, +y)
• Quadrant 2 : (-x, +y)
• Quadrant 3 : (-x, -y)
• Quadrant 4 : (+x, -y)

The point at which the axes intersect is known as the origin . The location of any point on a plane is expressed by a pair of values (x, y) and these pairs are known as the coordinates .

The figure below shows the Cartesian plane with coordinates (4,2). If the coordinates are identified, the distance between the two points and the interval’s midpoint that is connecting the points can be computed.

Coordinate Geometry Fig. 1: Cartesian Plane

Equation of a Line in Cartesian Plane

Equation of a line can be represented in many ways, few of which is given below-

(i) General Form

The general form of a line is given as Ax + By + C = 0.

(ii) Slope intercept Form 

Let x, y be the coordinate of a point through which a line passes, m be the slope of a line, and c be the y-intercept, then the equation of a line is given by:

(iii) Intercept Form of a Line

Consider a and b be the x-intercept and y-intercept respectively, of a line, then the equation of a line is represented as-

Slope of a Line: 

Consider the general form of a line Ax + By + C = 0, the slope can be found by converting this form to the slope-intercept form.

Ax + By + C = 0

⇒ By = − Ax – C

Comparing the above equation with y = mx + c,

Thus, we can directly find the slope of a line from the general equation of a line.

Coordinate Geometry Formulas and Theorems

Distance formula: to calculate distance between two points.

Let the two points be A and B, having coordinates to be (x 1 , y 1 ) and (x 2 , y 2 ), respectively.

Thus, the distance between two points is given as-

Coordinate Geometry Fig. 2: Distance Formula

Midpoint Theorem: To Find Mid-point of a Line Connecting Two Points

Consider the same points A and B, which have coordinates (x 1 , y 1 ) and (x 2 , y 2 ), respectively. Let M(x,y) be the midpoint of lying on the line connecting these two points A and B. The coordinates of point M is given as-

Angle Formula: To Find The Angle Between Two Lines

Consider two lines A and B, having their slopes m 1 and m 2, respectively.

Let “θ” be the angle between these two lines, then the angle between them can be represented as-

Special Cases:

• Case 1:  When the two lines are parallel to each other,

m 1 = m 2 = m

Substituting the value in the equation above,

• Case 2:  When the two lines are perpendicular to each other,

m 1 . m 2 = -1

Substituting the value in the original equation,

\(\begin{array}{l}\large \tan \theta = \frac{m_{1} – m_{2}}{1 + (-1)} = \frac{m_{1} – m_{2}}{0}\end{array} \) which is undefined.

Section Formula: To Find a Point Which Divides a Line into m:n Ratio

Consider a line A and B having coordinates (x 1 , y 1 ) and (x 2 , y 2 ), respectively. Let P be a point that which divides the line in the ratio m:n, then the coordinates of the coordinates of the point P is given as-

• When the ratio m:n is internal:
• When the ratio m:n is external:

Students can follow the link provided to learn more about the section formula  along its proof and solved examples.

Area of a Triangle in Cartesian Plane

The area of a triangle In coordinate geometry whose vertices are (x 1 , y 1 ), (x 2 , y 2 ) and (x 3 , y 3 ) is

If the area of a triangle whose vertices are (x 1 , y 1 ),(x 2 , y 2 ) and (x 3 , y 3 ) is zero, then the three points are collinear.

• Important:  Click here to Download  Co-ordinate Geometry pdf

Examples Based On Coordinate Geometry Concepts

Examples 1: Find the distance between points M (4,5) and N (-3,8).

Applying the distance formula we have,

Example 2: Find the equation of a line parallel to 3x+4y = 5 and passing through points (1,1).

For a line parallel to the given line, the slope will be of the same magnitude.

Thus the equation of a line will be represented as 3x+4y=k

Substituting the given points in this new equation, we have

k = 3 × 1 + 4 × 1 = 3 + 4 = 7

Therefore the equation is 3x + 4y = 7

Coordinate Geometry Questions For Practice

• Calculate the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, – 2) and B(3, 7).
• Find the area of the triangle having vertices at A, B, and C which are at points (2, 3), (–1, 0), and (2, – 4), respectively. Also, mention the type of triangle.
• A point A is equidistant from B(3, 8) and C(-10, x). Find the value for x and the distance BC.

Video Lesson on Coordinate Geometry Toughest Problems

Continue Learning

Frequently asked questions, what is abscissa and ordinates in coordinate geometry.

The abscissa and ordinate is used to represent the position of a point on a graph. The horizontal value or the X axis value is the abscissa while the vertical value i.e. the Y axis value is the ordinate. For example, in an ordered pair (2, 3), 2 is abscissa and 3 is ordinate.

What is a Cartesian Plane?

A Cartesian plane is a plane which is formed by two perpendicular lines known as the x-axis (horizontal axis) and the y-axis (vertical axis). The exact position of a point in Cartesian plane can be determined using the ordered pair (x, y).

Why do we Need Coordinate Geometry?

Coordinate geometry has various applications in real life. Some of the areas where coordinate geometry is an integral part include.

• In digital devices like computers, mobile phones, etc. to locate the position of cursor or finger.
• In aviation to determine the position and location of airplanes accurately.
• In maps and in navigation (GPS).
• To map geographical locations using latitudes and longitudes.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

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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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Case Study Questions for Class 9 Maths Chapter 3 Coordinate Geometry

• Last modified on: 1 year ago
• Reading Time: 2 Minutes

Case Study Questions

Question 1:

Saumya has to reach her office every day at 10:00 am. On the way to her office, she drops her son at school. Now, the location of Saumya’s house, her son’s school and her office are represented by the map below. Using the details given, answer the following questions.

Q1. Find the coordinates of Saumya’s home. (a) (1, 4) (b) (4, 1) (c) (7, 1) (d) (1, 7)

Q2. Find the coordinates of Saumya’s office. (a) (7, 5) (b) (5, 7) (c) (7, 1) (d) (1, 7)

Q3. Find the coordinates of Saumya’s son’s school. (a) (1, 4) (b) (4, 1) (c) (7, 1) (d) (1, 7)

Q4. Find the distance between Saumya’s home and her son’s school. (a) 7km (b) 4km (c) 3km (d) 1km

Q5. Find the distance between Saumya’s office and her son’s school. (a) 7km (b) 4km (c) 3km (d) 1km

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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
• Chapter 2 Polynomials Case Study Questions
• Chapter 4 Linear Equations in Two Variables Case Study Questions
• Chapter 5 Euclids Geometry Case Study Questions

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CBSE Class 9 Maths Case Study Questions PDF Download

Download Class 9 Maths Case Study Questions to prepare for the upcoming CBSE Class 9 Exams 2023-24. These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 9 so that they can score 100% in Exams.

Case study questions play a pivotal role in enhancing students’ problem-solving skills. By presenting real-life scenarios, these questions encourage students to think beyond textbook formulas and apply mathematical concepts to practical situations. This approach not only strengthens their understanding of mathematical concepts but also develops their analytical thinking abilities.

Table of Contents

CBSE Class 9th MATHS: Chapterwise Case Study Questions

Inboard exams, students will find the questions based on assertion and reasoning. Also, there will be a few questions based on case studies. In that, a paragraph will be given, and then the MCQ questions based on it will be asked. For Class 9 Maths Case Study Questions, there would be 5 case-based sub-part questions, wherein a student has to attempt 4 sub-part questions.

Chapterwise Case Study Questions of Class 9 Maths

• Case Study Questions for Chapter 1 Number System
• Case Study Questions for Chapter 2 Polynomials
• Case Study Questions for Chapter 3 Coordinate Geometry
• Case Study Questions for Chapter 4 Linear Equations in Two Variables
• Case Study Questions for Chapter 5 Introduction to Euclid’s Geometry
• Case Study Questions for Chapter 6 Lines and Angles
• Case Study Questions for Chapter 7 Triangles
• Case Study Questions for Chapter 8 Quadrilaterals
• Case Study Questions for Chapter 9 Areas of Parallelograms and Triangles
• Case Study Questions for Chapter 10 Circles
• Case Study Questions for Chapter 11 Constructions
• Case Study Questions for Chapter 12 Heron’s Formula
• Case Study Questions for Chapter 13 Surface Area and Volumes
• Case Study Questions for Chapter 14 Statistics
• Case Study Questions for Chapter 15 Probability

Checkout: Class 9 Science Case Study Questions

And for mathematical calculations, tap Math Calculators which are freely proposed to make use of by calculator-online.net

The above  Class 9 Maths Case Study Question s will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 9 Maths Case Study Questions have been developed by experienced teachers of cbseexpert.com for the benefit of Class 10 students.

Class 9 Maths Syllabus 2023-24

UNIT I: NUMBER SYSTEMS

1. REAL NUMBERS (18 Periods)

1. Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers.

2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number.

3. Definition of nth root of a real number.

4. Rationalization (with precise meaning) of real numbers of the type

(and their combinations) where x and y are natural number and a and b are integers.

5. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.)

UNIT II: ALGEBRA

1. POLYNOMIALS (26 Periods)

Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of ax2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. Recall of algebraic expressions and identities. Verification of identities:

RELATED STORIES

and their use in factorization of polynomials.

2. LINEAR EQUATIONS IN TWO VARIABLES (16 Periods)

Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax + by + c=0.Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line.

UNIT III: COORDINATE GEOMETRY COORDINATE GEOMETRY (7 Periods)

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations.

UNIT IV: GEOMETRY

1. INTRODUCTION TO EUCLID’S GEOMETRY (7 Periods)

History – Geometry in India and Euclid’s geometry. Euclid’s method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Showing the relationship between axiom and theorem, for example: (Axiom)

1. Given two distinct points, there exists one and only one line through them. (Theorem)

2. (Prove) Two distinct lines cannot have more than one point in common.

2. LINES AND ANGLES (15 Periods)

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180O and the converse.

2. (Prove) If two lines intersect, vertically opposite angles are equal.

3. (Motivate) Lines which are parallel to a given line are parallel.

3. TRIANGLES (22 Periods)

1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence).

2. (Prove) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).

3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).

4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (RHS Congruence)

5. (Prove) The angles opposite to equal sides of a triangle are equal.

6. (Motivate) The sides opposite to equal angles of a triangle are equal.

4. QUADRILATERALS (13 Periods)

1. (Prove) The diagonal divides a parallelogram into two congruent triangles.

2. (Motivate) In a parallelogram opposite sides are equal, and conversely.

3. (Motivate) In a parallelogram opposite angles are equal, and conversely.

4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.

5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.

6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and in half of it and (motivate) its converse.

5. CIRCLES (17 Periods)

1. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.

2. (Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.

3. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.

4. (Prove) The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

5. (Motivate) Angles in the same segment of a circle are equal.

6. (Motivate) If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.

7. (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

UNIT V: MENSURATION 1.

1. AREAS (5 Periods)

Area of a triangle using Heron’s formula (without proof)

2. SURFACE AREAS AND VOLUMES (17 Periods)

Surface areas and volumes of spheres (including hemispheres) and right circular cones.

UNIT VI: STATISTICS & PROBABILITY

STATISTICS (15 Periods)

 Bar graphs, histograms (with varying base lengths), and frequency polygons.

To crack case study questions, Class 9 Mathematics students need to apply their mathematical knowledge to real-life situations. They should first read the question carefully and identify the key information. They should then identify the relevant mathematical concepts that can be applied to solve the question. Once they have done this, they can start solving the Class 9 Mathematics case study question.

Benefits of Practicing CBSE Class 9 Maths Case Study Questions

Regular practice of CBSE Class 9 Maths case study questions offers several benefits to students. Some of the key advantages include:

• Deeper Understanding : Case study questions foster a deeper understanding of mathematical concepts by connecting them to real-world scenarios. This improves retention and comprehension.
• Practical Application : Students learn to apply mathematical concepts to practical situations, preparing them for real-life problem-solving beyond the classroom.
• Critical Thinking : Case study questions require students to think critically, analyze data, and devise appropriate solutions. This nurtures their critical thinking abilities, which are valuable in various academic and professional domains.
• Exam Readiness : By practicing case study questions, students become familiar with the question format and gain confidence in their problem-solving abilities. This enhances their readiness for CBSE Class 9 Maths exams.
• Holistic Development: Solving case study questions cultivates not only mathematical skills but also essential life skills like analytical thinking, decision-making, and effective communication.

Tips to Solve CBSE Class 9 Maths Case Study Questions Effectively

Solving case study questions can be challenging, but with the right approach, you can excel. Here are some tips to enhance your problem-solving skills:

• Read the case study thoroughly and understand the problem statement before attempting to solve it.
• Identify the relevant data and extract the necessary information for your solution.
• Break down complex problems into smaller, manageable parts to simplify the solution process.
• Apply the appropriate mathematical concepts and formulas, ensuring a solid understanding of their principles.
• Clearly communicate your solution approach, including the steps followed, calculations made, and reasoning behind your choices.
• Practice regularly to familiarize yourself with different types of case study questions and enhance your problem-solving speed.Class 9 Maths Case Study Questions

Remember, solving case study questions is not just about finding the correct answer but also about demonstrating a logical and systematic approach. Now, let’s explore some resources that can aid your preparation for CBSE Class 9 Maths case study questions.

Q1. Are case study questions included in the Class 9 Maths Case Study Questions syllabus?

Yes, case study questions are an integral part of the CBSE Class 9 Maths syllabus. They are designed to enhance problem-solving skills and encourage the application of mathematical concepts to real-life scenarios.

Q2. How can solving case study questions benefit students ?

Solving case study questions enhances students’ problem-solving skills, analytical thinking, and decision-making abilities. It also bridges the gap between theoretical knowledge and practical application, making mathematics more relevant and engaging.

Q3. How do case study questions help in exam preparation?

Case study questions help in exam preparation by familiarizing students with the question format, improving analytical thinking skills, and developing a systematic approach to problem-solving. Regular practice of case study questions enhances exam readiness and boosts confidence in solving such questions.

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Chapter 7 Class 10 Coordinate Geometry

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Updated for new NCERT Book for 2023-2024 Boards.

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 10th Standard Maths Subject Coordinate Geometry Case Study Questions 2021

QB365 Provides the updated CASE Study Questions for Class 10 Maths, 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

QB365 - Question Bank Software

10th Standard CBSE

Final Semester - June 2015

Case Study Questions

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

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

(iv) Which of the following is true?

(v) How far is the school from Alia's house than Shaguns house?

(ii) The value of x is equal to

(iii) If M is any point exactly in between city A and city B, then coordinates of M are

(iv) The ratio in which A divides the line segment joining the points O and M is

(v) If the person analyse the petrol at the point M(the mid point of AB), then what should be his decision?

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

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

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

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

(ii) The centre of circle is the

(iii) The radius of the circle is

(iv) The area of the circle is

(v) If  \(\left(1, \frac{\sqrt{7}}{3}\right)\)   is one of the ends of a diameter, then its other end is

(ii) If S be the mid-point of line joining P and Q, then coordinates of S are

(iii) If T be the mid-point of line joining Rand Q, then coordinates of T are

(iv) If Ube the mid-point of line joining Rand P, then coordinates of U are

(v) The coordinates of centroid of \(\Delta\) STU are

*****************************************

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10th Class Mathematics Coordinate Geometry Question Bank

Done case based (mcqs) - coordinate geometry total questions - 35.

A) \[(2,3)\] and\[(6,5)\] done clear

B) \[(3,2)\] and \[(5,6)\] done clear

C) \[(3,6)\] and\[(5,2)\] done clear

D) \[(6,3)\] and \[(2,5)\] done clear

question_answer 2) What is the distance between Golu and Monu?

A) \[\sqrt{5}\] units done clear

B) \[2\sqrt{5}\] units done clear

C) \[3\sqrt{5}\] units done clear

D) \[4\sqrt{5}\] units done clear

question_answer 3) What will be the coordinates of a point exactly between Sonu and Goru where a person can be seated?

A)  \[\left( \frac{5}{2},\frac{9}{2} \right)\] done clear

B)  \[\left( \frac{11}{2},\frac{7}{2} \right)\] done clear

C)  \[(4,4)\] done clear

D)  \[\left( \frac{9}{2},4 \right)\] done clear

question_answer 4) Find the area covered by Sonu and its members, if all four seats connected with a rope.

A) \[\text{2}\sqrt{5}\,\text{sq}.\]units done clear

B) \[\sqrt{10}\,\text{sq}.\] units done clear

C) \[2\sqrt{10}\,\text{sq}.\] units done clear

D)  \[10\,\text{sq}.\] units done clear

question_answer 5) If the doctor divides the rope joining Sonu and Goru in the ratio \[1:2,\] then the coordinates of the seat of the doctor is:

A)  \[\left( \frac{10}{3},\frac{11}{3} \right)\] done clear

B)  \[\left( \frac{11}{3},\frac{10}{3} \right)\] done clear

D)  \[(3,4)\] done clear

A) \[\sqrt{41}\] units done clear

B)  3 units done clear

C)  6 units done clear

D)  7 units done clear

question_answer 7) Suppose point \[D(1,4)\] divide the line segment AB in the ratio \[k:1,\] then find the value of k.

A) \[3\] done clear

B) \[3/2\] done clear

C) \[2\] done clear

D)  \[1/2\] done clear

question_answer 8) If we draw perpendicular lines from points A and B to the X-axis. the region covered by these perpendicular lines is:

A)  4 sq. units done clear

B)  5 sq. units done clear

C)  20 sq. units done clear

D)  10 sq. units done clear

question_answer 9) Find the area of \[\Delta ABC\].

question_answer 10) Find the image of the mid-point of AB with respect ro X-axis.

A)  \[\left( \frac{1}{2},-4 \right)\] done clear

B)  \[\left( -\frac{1}{2},4 \right)\] done clear

C)  \[\left( \frac{1}{2},4 \right)\] done clear

D)  \[\left( -\frac{1}{2},-4 \right)\] done clear

A)  \[(4,9)\] done clear

B)  \[(5,9)\] done clear

C)  \[\left( \frac{9}{2},9 \right)\] done clear

D)  \[(4,8)\] done clear

question_answer 12) The type of triangle ABC is:

A)  equilateral triangle done clear

B)  isosceles triangle done clear

C)  scalene triangle done clear

D)  right triangle done clear

question_answer 13) The area of triangle RBP is:

A)  2 sq. units done clear

B)  4 sq. units done clear

C)  \[\frac{3}{2}sq.\] units done clear

D)  5 sq, units done clear

question_answer 14) The area of rectangle BCED is:

A)  8 sq. units done clear

B)  10 sq. units done clear

C)  12 sq. units done clear

D)  16 sq. units done clear

question_answer 15) The area of trapezium DEGF is:

A) \[(5,3)\] done clear

B) \[(6,3)\] done clear

C)  \[\left( \frac{11}{2},3 \right)\] done clear

D)  \[\left( 7,3 \right)\] done clear

question_answer 17) The distance between P and R is:

A)  3 units done clear

B) \[3.5\]units done clear

C)  \[3\sqrt{5}\] units done clear

D)  \[5\sqrt{5}\]units done clear

question_answer 18) The area of the triangle PQR is:

A)  21 sq. units done clear

B)  35 sq. units done clear

C)  42 sq, units done clear

D)  45 sq, units done clear

question_answer 19) The point on X-axis, which is equidistant from points Q and R is:

A)  \[\left( \frac{11}{2},0 \right)\] done clear

B)  \[(5,0)\] done clear

C)  \[(6,0)\] done clear

D)  \[(5,3)\] done clear

question_answer 20) The centroid of the triangle PQR is:

A)  \[(5,5)\] done clear

B) \[(6,5)\] done clear

C)  \[\left( \frac{17}{3},4 \right)\] done clear

D)  \[\left( \frac{17}{3},5 \right)\] done clear

A)  \[(1,5),\,(4,6),\,(7,2)\] done clear

B)  \[(2,4),\,(3,5),\,(6,3)\] done clear

C)  \[(1,4),\,(4,5),\,(7,3)\] done clear

D)  None of these done clear

question_answer 22) The perimeter of \[\Delta PQR\] is:

A)  \[(\sqrt{10}+5+3\sqrt{5})\] units done clear

B)    \[(\sqrt{10}+8\sqrt{5})\] units done clear

C)  \[(10+3\sqrt{5})\] units done clear

D)  \[(\sqrt{10}+5\sqrt{3})\] units done clear

question_answer 23) The coordinates of the point M on PR such that \[\text{PM}:\text{MR}=\text{2}:\text{1},\]is:

A) \[(4,3)\] done clear

B) \[(5,3)\] done clear

C) \[(5,4)\] done clear

D)  \[(2,3)\] done clear

question_answer 24)   What will be the coordinates of the vertices of \[\Delta PQR\] if C is the origin?

A)  \[(14,3),\,(11,2),(8,6)\] done clear

B)  \[(15,4),\,(12,3),(9,7)\] done clear

C)  \[(14,2),\,(11,1),(8,5)\] done clear

D)  \[(15,3),\,(12,2),(9,6)\] done clear

question_answer 25) What are the coordinates of P if D is taken as the origin?

A)  \[(-15,5)\] done clear

B) \[(15,5)\] done clear

C)  \[(15,7)\] done clear

D)  \[(15,3)\] done clear

A) \[(20,3)\] done clear

B) \[(3,20)\] done clear

C) \[(80,3)\] done clear

D) \[(3,80)\] done clear

question_answer 27) The coordinates of the blue flag is:

A) \[(7,16)\] done clear

B) \[(16,7)\] done clear

C) \[(80,7)\] done clear

D)  \[(7,80)\] done clear

question_answer 28) What is the distance between both the flags?

A) \[2\sqrt{2}m\] done clear

B) \[3\sqrt{2}m\]   done clear

C) \[4\sqrt{2}m\] done clear

D) \[5\sqrt{2}m\] done clear

question_answer 29) If Raman has to post a green flag exactly halfway between the line segment joining the two flags, where should he post his flag?

A)  16m on 4th line done clear

B)  16m on 5th line done clear

C)  18 m on 4th line done clear

D)  18m on 5th line done clear

question_answer 30) If Raman change his position and post a green flag at a point between the line segment joining the two flags, then the coordinate of the green flag which divides the Line : segment internally in the ratio \[1:2\] is:

A)  \[\left( \frac{13}{3},\frac{56}{3} \right)\] done clear

B)  \[\left( \frac{56}{3},\frac{13}{3} \right)\] done clear

C)  \[\left( \frac{13}{4},\frac{56}{3} \right)\] done clear

D)  \[\left( \frac{56}{3},\frac{13}{4} \right)\] done clear

A)  \[(7,6),\,(4,5),(1,2)\]and \[(4,3)\] done clear

B)  \[(1,2),(4,3),(7,6)\]and \[(4,5)\] done clear

C)  \[(4,5),(7,6),(4,3)\]and \[(1,2)\] done clear

D)  None of the above done clear

question_answer 32) When the points P, Q, R and S (in order) join together, it form a quadrilateral PQRS. The relation between the sides of quadrilateral PQRS is:

A) \[\text{QR}=S\text{P}\] and \[\text{PQ}=\text{RS}\] done clear

B) \[\text{PQ}=\text{QR}\] and \[\text{RS}=S\text{P}\] done clear

C) \[\text{PQ},\text{ QR},\text{ RS}\] and \[SP\] all are different done clear

question_answer 33) The Length of the diagonals PR and QS are:

A) \[\sqrt{10}\]and \[\sqrt{8}\]respectively done clear

B) \[2\] and \[\sqrt{52}\] respectively done clear

C) \[\sqrt{2}\] and \[\sqrt{10}\] respectively done clear

question_answer 34) The quadrilateral PQRS formed by these points is:

A)  a square done clear

B)  a rectangle done clear

C)  a parallelogram done clear

D)  a trapezium done clear

question_answer 35) The height of the quadrilateral PQRS taking SR as the base is:

A)  \[\frac{\sqrt{10}}{5}\]units done clear

B)  \[\frac{2\sqrt{10}}{5}\]units done clear

C)  \[3\sqrt{10}\]units done clear

D)  \[\frac{3\sqrt{10}}{5}\]units done clear

Study Package

Case Based (MCQs) - Coordinate Geometry

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