Question

The ratio in which the line segment joining the points $A(1,–7)$ and $B(6,4)$ is divided by 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 $C(x,0)$ 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 $7:4$.