CBSE Class 9 Maths Chapter 1: Orienting Yourself: The Use of Coordinates — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 1: Orienting Yourself: The Use of Coordinates from the NCERT Class 9 Mathematics textbook. Each question has four options - read both the Assertion (A) and Reason (R) carefully before selecting your answer.
How to attempt Assertion & Reason questions:
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Assertion & Reason Questions
1
Assertion (A): Two coordinates are required to locate a general point in a two-dimensional Cartesian plane.
Reason (R): The coordinates give the point's directed distances relative to two perpendicular axes.
Reason (R): The coordinates give the point's directed distances relative to two perpendicular axes.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The two independent directions specify the horizontal and vertical position uniquely.
2
Assertion (A): The x-axis is horizontal and the y-axis is vertical in the Cartesian plane.
Reason (R): The intersection of the two axes is called the origin.
Reason (R): The intersection of the two axes is called the origin.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are correct, but naming their intersection does not explain their orientations.
3
Assertion (A): The coordinates of the origin are (0, 0).
Reason (R): The origin lies in the first quadrant because both of its coordinates are non-negative.
Reason (R): The origin lies in the first quadrant because both of its coordinates are non-negative.
Answer: (c)
A is true, but R is false. The origin lies on both axes and is not part of any quadrant.
4
Assertion (A): The point (0, 5) lies on the x-axis.
Reason (R): Every point whose x-coordinate is zero lies on the y-axis.
Reason (R): Every point whose x-coordinate is zero lies on the y-axis.
Answer: (d)
A is false, but R is true. Since its x-coordinate is zero, (0, 5) is on the y-axis.
5
Assertion (A): A point in Quadrant III has both coordinates negative.
Reason (R): Quadrant III lies to the left of the y-axis and below the x-axis.
Reason (R): Quadrant III lies to the left of the y-axis and below the x-axis.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Left gives a negative x-coordinate and below gives a negative y-coordinate.
6
Assertion (A): A point on the x-axis has coordinates of the form (x, 0).
Reason (R): A point on the y-axis has coordinates of the form (0, y).
Reason (R): A point on the y-axis has coordinates of the form (0, y).
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are correct, but the second axis rule does not explain the first.
7
Assertion (A): A point in Quadrant II has a negative x-coordinate and a positive y-coordinate.
Reason (R): The x-coordinate measures distance from the x-axis.
Reason (R): The x-coordinate measures distance from the x-axis.
Answer: (c)
A is true, but R is false. The x-coordinate is the directed distance from the y-axis; the y-coordinate relates to the x-axis.
8
Assertion (A): The point (-3, -4) lies in Quadrant IV.
Reason (R): A point with both coordinates negative lies in Quadrant III.
Reason (R): A point with both coordinates negative lies in Quadrant III.
Answer: (d)
A is false, but R is true. Quadrant IV has positive x and negative y, whereas (-3, -4) is in Quadrant III.
9
Assertion (A): The distance between (x1, y) and (x2, y) is |x2 - x1|.
Reason (R): The points have the same y-coordinate, so their separation is entirely horizontal.
Reason (R): The points have the same y-coordinate, so their separation is entirely horizontal.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Only the change in x contributes to their distance.
10
Assertion (A): The ordered pairs (2, 5) and (5, 2) usually represent different points.
Reason (R): The distance formula can be derived from the Baudhāyana-Pythagoras theorem.
Reason (R): The distance formula can be derived from the Baudhāyana-Pythagoras theorem.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are true, but the distance formula does not explain why coordinate order matters.
11
Assertion (A): The distance between two distinct points is always positive.
Reason (R): For points on a horizontal line, the distance is x2 - x1 without using an absolute value, regardless of their order.
Reason (R): For points on a horizontal line, the distance is x2 - x1 without using an absolute value, regardless of their order.
Answer: (c)
A is true, but R is false. An absolute value is required so that reversing the order does not produce a negative distance.
12
Assertion (A): The distance between (x1, y1) and (x2, y2) is |x2 - x1| + |y2 - y1|.
Reason (R): The Cartesian distance is sqrt((x2 - x1)^2 + (y2 - y1)^2).
Reason (R): The Cartesian distance is sqrt((x2 - x1)^2 + (y2 - y1)^2).
Answer: (d)
A is false, but R is true. The straight-line distance follows the Pythagorean relationship, not the sum of horizontal and vertical changes.
13
Assertion (A): The general distance formula follows by treating the horizontal and vertical coordinate differences as perpendicular sides of a right triangle.
Reason (R): The hypotenuse length is found using the Baudhāyana-Pythagoras theorem.
Reason (R): The hypotenuse length is found using the Baudhāyana-Pythagoras theorem.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Applying the theorem gives the square root of the sum of the squared coordinate differences.
14
Assertion (A): Reflecting a point in the y-axis changes the sign of its x-coordinate but not its y-coordinate.
Reason (R): Reflection preserves distances and lengths.
Reason (R): Reflection preserves distances and lengths.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both facts are true, but preservation of length alone does not specify which coordinate changes sign.
15
Assertion (A): Three points can be tested for collinearity by checking whether the distance between the two outer points equals the sum of the other two distances.
Reason (R): Every set of three points determines a unique circle.
Reason (R): Every set of three points determines a unique circle.
Answer: (c)
A is true, but R is false. Only three non-collinear points determine a unique circle; collinear points do not.
16
Assertion (A): A unique circle passes through any three points, even when all three are collinear.
Reason (R): Three non-collinear points determine a unique circumcircle.
Reason (R): Three non-collinear points determine a unique circumcircle.
Answer: (d)
A is false, but R is true. Non-collinearity is necessary for the perpendicular bisectors to meet at a finite circle centre.
17
Assertion (A): The midpoint of a segment is obtained by averaging the corresponding coordinates of its endpoints.
Reason (R): The midpoint divides the segment into two equal lengths.
Reason (R): The midpoint divides the segment into two equal lengths.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Coordinate averaging locates the point halfway in both the horizontal and vertical directions.
18
Assertion (A): A scale such as 1 cm : 1 foot can represent a room on a coordinate grid.
Reason (R): A Cartesian plane is divided into four quadrants by its axes.
Reason (R): A Cartesian plane is divided into four quadrants by its axes.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are correct, but the quadrant division does not explain how a drawing scale represents actual lengths.
19
Assertion (A): If M is the midpoint of endpoints (x1, y1) and (x2, y2), then M is ((x1 + x2)/2, (y1 + y2)/2).
Reason (R): The midpoint must always have the same coordinates as one of the endpoints.
Reason (R): The midpoint must always have the same coordinates as one of the endpoints.
Answer: (c)
A is true, but R is false. It coincides with an endpoint only in a degenerate segment whose endpoints are the same.
20
Assertion (A): Negative coordinates prevent a coordinate system from representing real locations.
Reason (R): Negative and positive coordinates allow points to be located on opposite sides of the two axes.
Reason (R): Negative and positive coordinates allow points to be located on opposite sides of the two axes.
Answer: (d)
A is false, but R is true. Negative values extend the grid left of the y-axis and below the x-axis rather than preventing location.
❓ Frequently Asked Questions
What is covered in CBSE Class 9 Maths Chapter 1 Orienting Yourself: The Use of Coordinates?
This chapter covers all key topics from Orienting Yourself: The Use of Coordinates as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 9 board exam preparation covering the complete syllabus.
Are these CBSE Class 9 Maths Assertion & Reason updated for 2026-27?
Yes, all content at eBookPublisher is updated as per the latest 2026-27 CBSE syllabus.
How many chapters are in CBSE Class 9 Maths?
All chapters of CBSE Class 9 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
Can I study Orienting Yourself: The Use of Coordinates online for free?
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