Assertion (A): The point which divides the line segment joining the points A(1, 2) and B(–1, 1) internally in the ratio 1 : 2 is ((-1)/(3), 5/3 ). Reason (R): The coordinates of the point which divides the line segment joining the points A(x_1, y_1) and B(x_2, y_2) in the ratio m_1 : m_2 are ((m_1x_2 + m_2x_1)/(m_1 + m_2), (m_1y_2 + m_2y_1)/(m_1 + m_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 30/3/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2024: question 19

Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, 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): The point which divides the line segment joining the points A(1, 2) and B(–1, 1) internally in the ratio 1 : 2 is $(\frac{- 1}{3}, \frac{5}{3})$ .

Reason (R): The coordinates of the point which divides the line segment joining the points A $(x_{1}, y_{1})$ and B $(x_{2}, y_{2})$ in the ratio $m_{1} : m_{2}$ are $(\frac{m _{1} x _{2} + m _{2} x _{1}}{m _{1} + m _{2}}, \frac{m _{1} y _{2} + m _{2} y _{1}}{m _{1} + m _{2}})$ .

(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 30/3/1.

Hints

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

Hint 1

Apply the formula given in R to the points in A.

Hint 2

Check the sign of the x-coordinate.

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.

Using the section formula with $m_{1} : m_{2} = 1 : 2$ : $x = \frac{1 ( - 1 ) + 2 ( 1 )}{3} = \frac{1}{3}$ and $y = \frac{1 ( 1 ) + 2 ( 2 )}{3} = \frac{5}{3}$ .
The point is $(\frac{1}{3}, \frac{5}{3})$ , not $(- \frac{1}{3}, \frac{5}{3})$ , so A is false. R is the correct section formula, so R is true. The answer is option (D).
1 mark

Answer: Option (D)

Where the marks are

Shows A is false and R is true, option (D) (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 30/3/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2024: question 19

Hints

Step-by-step solution

Revise the chapter

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