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

Let the x-axis divide the line segment joining A(−6, 5) and B(−4, −1) in the ratio k : 1.

Since the point lies on the x-axis, its y-coordinate = 0.

Using the section formula for the y-coordinate:

$$\frac{k(-1) + 1(5)}{k + 1} = 0$$

$$-k + 5 = 0 \implies k = 5$$

So the ratio is 5 : 1.

Now, the x-coordinate of the point of intersection:

$$x = \frac{5(-4) + 1(-6)}{5 + 1} = \frac{-20 - 6}{6} = \frac{-26}{6} = \frac{-13}{3}$$

The x-axis divides the segment in the ratio 5 : 1, and the point of intersection is $\left(\dfrac{-13}{3},\ 0\right)$.

Source: Chapter 7, Section 7.3 (Section Formula)

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• A point on the x-axis always has y-coordinate = 0. Use this condition with the section formula to find the ratio k.
• Once k is known, substitute back to find the x-coordinate.
• Examiners expect you to clearly state both the ratio and the coordinates of the point. Missing either loses a mark.