Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1 : 1. Reason (R): The ratio in which the point (– 3, k) divides the line segment joining the points (– 5, 4) and (– 2, 3) is 1 : 2. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the 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.

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/4/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2024: question 19

Set in the CBSE Class 10 board exam of 2024, paper 30/4/1, section A, question 19, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q19 · 1 mark · Assertion-reasonCompetency-basedCoordinate Geometry

Assertion (A): Mid-point of a line segment divides the line segment in the ratio $1 : 1$ .

Reason (R): The ratio in which the point $(-3, k)$ divides the line segment joining the points $(-5, 4)$ and $(-2, 3)$ is $1 : 2$ .

(A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the 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.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/4/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Check the assertion from the definition of mid-point.

Hint 2

Use the section formula on x-coordinates to find the ratio in R.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

A is true: the mid-point is equidistant from both ends, so ratio 1 : 1.
R: with ratio $k : 1$ , $\frac{- 2 k - 5}{k + 1} = - 3 \Rightarrow k = 2$ , so the ratio is 2 : 1, not 1 : 2. R is false. Option (C).
1 mark

Answer: Option (C)

Where the marks are

Shows ratio is 2 : 1 so R false, A true (1 mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Section Formula (Internal Division)

Practise this chapterBoard-style questions from Coordinate Geometry, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2024: question 19

Hints

Step-by-step solution

Revise the chapter

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