Q1. [1] § 7.4 Summary
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.
Select the correct answer from the codes (A), (B), (C) and (D) as given below.
- 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 30/4/1 Q19
Generated by claude-sonnet-4-6 · 2026-06-15 10:29 · grounding rag
Model Answer
(C) Assertion (A) is true, but Reason (R) is false.
Assertion is true (mid-point divides in ratio 1:1). For Reason, using section formula with ratio 1:2: x = [1(−2)+2(−5)]/(1+2) = −4 ≠ −3, so the ratio is incorrect.
Explanation
- Assertion is directly confirmed by the Special Case in Section 7.3: the mid-point divides in ratio 1:1. ✓
- Reason: Verify by applying the section formula. With ratio 1:2, x-coordinate = $\frac{1(-2)+2(-5)}{3} = \frac{-12}{3} = -4 \neq -3$. The correct ratio is actually 2:1 (check: $\frac{2(-2)+1(-5)}{3} = -3$ ✓). So Reason is false.
- Hence answer is (C).
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