Find the ratio in which $y$-axis divides the line segment joining the points $(5, -6)$ and $(-1, -4)$.
Generated by claude-sonnet-4-6 · 2026-06-15 10:30 · grounding rag
Model Answer
Let the y-axis divide the segment joining A(5, –6) and B(–1, –4) in the ratio $k : 1$.
Since any point on the y-axis has x-coordinate = 0, using the section formula:
$$x = \frac{k \cdot (-1) + 1 \cdot 5}{k + 1} = 0$$
$$-k + 5 = 0 \implies k = 5$$
∴ The required ratio is 5 : 1.
Source: Chapter 7, Section 7.3 (Section Formula)
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Explanation
- A point on the y-axis always has x-coordinate 0 — use this as the key condition.
- Apply section formula only for x-coordinate; setting it equal to 0 gives k directly.
- Examiners expect you to state the ratio clearly at the end. No need to find the y-coordinate unless asked.