Q1. [1]
Directions: Two statements are given, one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
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 $\left(\dfrac{-1}{3}, \dfrac{5}{3}\right)$.
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 $\left(\dfrac{m_1 x_2 + m_2 x_1}{m_1 + m_2},\ \dfrac{m_1 y_2 + m_2 y_1}{m_1 + m_2}\right)$.
- 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.
Previously asked in CBSE board exam
2024 30/3/1 Q19
Generated by claude-sonnet-4-6 · 2026-06-15 10:28 · grounding rag
Model Answer
(D) Assertion (A) is false, but Reason (R) is true.
Using the section formula with $m_1:m_2 = 1:2$, $A(1,2)$, $B(-1,1)$: $x = \dfrac{1(-1)+2(1)}{3} = \dfrac{1}{3}$, $y = \dfrac{1(1)+2(2)}{3} = \dfrac{5}{3}$. The correct point is $\left(\dfrac{1}{3}, \dfrac{5}{3}\right)$, not $\left(\dfrac{-1}{3}, \dfrac{5}{3}\right)$.
Explanation
The Reason (R) correctly states the Section Formula (from Chapter 7, Section 7.3). However, the Assertion (A) has a sign error in the x-coordinate. Applying the formula gives $x = \frac{1\times(-1)+2\times1}{1+2} = \frac{1}{3}$, not $\frac{-1}{3}$. So A is false, R is true → answer is (D).
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