Question

The ratio in which the line segment joining the points (1, – 7) and (6, 4) is divided by the x-axis is ___.

• A. 3:1
• B. 2:3
• C. 7:2
• D. 7:4

Answer 1

The correct option is D

7:4

Let us consider a point C(x, 0), that divides AB in the ratio k:1.

By section formula, the coordinates of C are given by: $(\frac{6k+1}{k+1},\frac{4k-7}{k+1})$

But C(x, 0) = $(\frac{6k+1}{k+1},\frac{4k-7}{k+1})$ $\Rightarrow \frac{4k-7}{k+1}$ = 0

$\Rightarrow 4k-7$ = 0 $\Rightarrow k$ = $\frac{7}{4}$

i.e., the x-axis divides AB in the ratio 7:4.