Mathematics — Standard (041) — CBSE Class 10 board question

Option D: 2 : 1

Let the x-axis divide AB in ratio $k:1$. The y-coordinate of the point on x-axis = 0.

$$\frac{k(-3) + 1(6)}{k+1} = 0 \Rightarrow -3k + 6 = 0 \Rightarrow k = 2$$

So the ratio is 2 : 1.

Source: Chapter 7, Section 7.3 (Section Formula)

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• A point on the x-axis has y-coordinate = 0. Use the section formula for the y-coordinate and set it equal to 0 to find $k$.
• Students often mix up which y-coordinate belongs to A and which to B — here A(3, 6) gives $y_1 = 6$ and B(−12, −3) gives $y_2 = −3$.
• The answer is D (2:1), not 1:2 — the x-axis is closer to B, so it divides in 2:1 from A's side.