Find the ratio in which the line segment joining the points A(6, 3) and B($-2$, $-5$) is divided by x-axis.
Generated by claude-sonnet-4-6 · 2026-06-15 10:32 · grounding rag
Model Answer
Let the x-axis divide AB in the ratio $k : 1$ at point P.
Since P lies on the x-axis, its y-coordinate = 0.
Using the section formula:
$$y = \frac{k \times (-5) + 1 \times 3}{k + 1} = 0$$
$$-5k + 3 = 0$$
$$k = \frac{3}{5}$$
So the ratio is $k : 1 = 3 : 5$.
The x-axis divides the line segment AB in the ratio 3 : 5.
Source: Chapter 7, Section 7.3 (Section Formula)
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Explanation
- A point on the x-axis always has y-coordinate = 0. Use this condition with the section formula to set up the equation.
- Assume the ratio as $k:1$ to reduce working to one variable.
- Examiners expect you to clearly state the section formula, substitute values, solve for $k$, and state the final ratio. All three steps must be shown for full marks.