Hello students, we are providing assertion reason questions for class 10. Assertion Reason questions are the new question format that is introduced in CBSE board. The resources for assertion reason questions are very less. So, to help students we have created chapterwise assertion reason questions for class 10 maths. In this article, you will find assertion reason questions for CBSE Class 10 Maths Chapter 7 Coordinate Geometry. It is a part of Assertion Reason Questions for CBSE Class 10 Maths Series.
| Chapter | Coordinate Geometry |
| Type of Questions | Assertion Reason Questions |
| Nature of Questions | Competency Based Questions |
| Board | CBSE |
| Class | 10 |
| Subject | Maths |
| Useful for | Class 10 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| Important Link | Class 10 Maths Chapterwise Assertion Reason |
Assertion Reason Questions on Coordinate Geometry
Assertion and Reason Questions
Directions: Each of the following questions consists of two statements: an Assertion (A) and a Reason (R). Answer them by selecting the correct option:
(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 Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.
Q1. Assertion (A): The distance between the points $A(3,4)$ and $B(0,0)$ is 5 units.
Reason (R): The distance formula between two points $\left(x_1, y_1\right)$ and $\left(x_2, y_2\right)$ is
$$
\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2} .
$$
Answer: Option (a) is correct.
Explanation: Applying the formula gives
$$
\sqrt{(3-0)^2+(4-0)^2}=\sqrt{9+16}=\sqrt{25}=5
$$
So both $A$ and $R$ are true and $R$ explains $A$.
Difficulty Level: Easy
Q2. Assertion (A): The midpoint of the segment joining $A(2,-3)$ and $B(4,5)$ is $(3,1)$.
Reason $(R)$ : The midpoint formula is
$$
\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right) .
$$
Answer: Option (a) is correct.
Explanation: Using the formula:
$$
\left(\frac{2+4}{2}, \frac{-3+5}{2}\right)=(3,1) .
$$
So both $A$ and $R$ are true and related.
Difficulty Level: Easy
Q3. Assertion (A): The coordinates of a point dividing the line segment joining $A(2,4)$ and $B(6,8)$ in the ratio $1: 1$ is $(4,6)$.
Reason (R): The section formula for internal division is
$$
\left(\frac{m x_2+n x_1}{m+n}, \frac{m y_2+n y_1}{m+n}\right) .
$$
Answer: Option (a) is correct.
Explanation: Substituting into the section formula gives
$$
\left(\frac{1 \times 6+1 \times 2}{2}, \frac{1 \times 8+1 \times 4}{2}\right)=(4,6) .
$$
So both statements are correct and linked.
Difficulty Level: Moderate
Q4. Assertion (A): The area of triangle with vertices $A(0,0), B(4,0), C(4,3)$ is 6 square units.
Reason $(\mathrm{R})$ : Area of triangle with coordinates $\left(x_1, y_1\right),\left(x_2, y_2\right),\left(x_3, y_3\right)$ is given by
$$
\frac{1}{2}\left|x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right| .
$$
Answer: Option (a) is correct.
Explanation: Substituting the values gives:
$$
\frac{1}{2}|0(0-3)+4(3-0)+4(0-0)|=\frac{1}{2}|0+12+0|=6 .
$$
Both statements are true and $R$ explains $A$.
Difficulty Level: Moderate
Q5. Assertion (A): If three points lie on a straight line, the area of the triangle formed by them is zero.
Reason (R): The coordinates of three collinear points satisfy the distance formula.
Answer: Option (c) is correct.
Explanation: The area of a triangle formed by three collinear points is zero. But satisfying the distance formula isn’t the correct explanation for that — it’s the area formula.
Difficulty Level: Tough
Also check
- Some Applications of Trigonometry Class 10 Assertion Reason Questions Maths Chapter 9
- Introduction to Trigonometry Class 10 Assertion Reason Questions Maths Chapter 8
- Coordinate Geometry Class 10 Assertion Reason Questions Maths Chapter 7
- Triangles Class 10 Assertion Reason Questions Maths Chapter 6
- Arithmetic Progressions Class 10 Assertion Reason Questions Maths Chapter 5
- Quadratic Equations Class 10 Assertion Reason Questions Maths Chapter 4
- Pair of Linear Equations in Two Variables Class 10 Assertion Reason Questions Maths Chapter 3
- Polynomials Class 10 Assertion Reason Questions Maths Chapter 2
- Real Numbers Class 10 Assertion Reason Questions Maths Chapter 1
Topics from which assertion reason questions may be asked
- Distance Formula
- Section Formula
- Midpoint Formula
Coordinate geometry connects algebra with visual representation of space.
Assertion reason questions from the above given topic may be asked.
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Frequently Asked Questions (FAQs) on Coordinate Geometry Assertion Reason Questions Class 10
Q1: What does the chapter ‘Coordinate Geometry’ cover?
A1: It builds key concepts related to coordinate geometry and prepares you for logical reasoning-based questions.
Q2: What are assertion reason questions?
A2: These consist of two statements: an assertion and a reason. Students need to determine their correctness and relationship.
Q3: Why practice assertion reason questions in Coordinate Geometry?
A3: They strengthen core concepts and boost confidence in tackling tricky scenarios from coordinate geometry.
Q4: Are assertion reason questions part of CBSE board exams?
A4: Yes, they are included under competency-based formats to test depth of understanding.
