Question

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

• A. 2:3
• B. 7:2
• C. 7:4
• D. 3:1

Answer 1

The correct option is C

7:4

Let $C(x,0)$ be the point on the x-axis that divides the line segment joining the points $A(1,-7)$ and $B(6,4)$ in the ratio $k:1$.

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

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

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

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