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Mathematics — CBSE Class 10 board question

Q1. [1]
The line segment joining the points $P(-4, -2)$ and $Q(10, 4)$ is divided by $y$-axis in the ratio
  1. (A) $2 : 5$
  2. (B) $1 : 2$
  3. (C) $2 : 1$
  4. (D) $5 : 2$
Previously asked in CBSE board exam
2026 30/5/1 Q2
Generated by claude-sonnet-4-6 · 2026-06-15 10:32 · grounding rag
Model Answer

(D) 5 : 2

Let the y-axis divide PQ in ratio k : 1. On the y-axis, x-coordinate = 0.
$$\frac{10k + (-4)}{k+1} = 0 \Rightarrow 10k = 4 \Rightarrow k = \frac{2}{5}$$
So ratio = 2/5 : 1 = 2 : 5… wait — (A) 2 : 5.

Source: Chapter 7, Section 7.3 (Section Formula)

Explanation

The y-axis has x = 0. Using section formula with ratio k : 1: set the x-coordinate expression $\frac{10k-4}{k+1}=0$, giving $k=\frac{2}{5}$, i.e., ratio = 2 : 5. The correct answer is (A) 2 : 5. Note: option (D) 5:2 is the trap — the ratio is P-side to Q-side, which is 2:5, not 5:2.

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