Question

Find the ratio in which the line segment joining A (6,4) and B(1,-7) is divided internally by x axis.

Answer 1

For x-axis $y=0$

Let the ratio be $k:1$

Then $\frac{k{x}_2+1\times x_1}{k+1}=a$, $\frac{k{y}_2+1\times y_1}{k+1}=0$

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

$\Rightarrow -7k+4=0$

$\Rightarrow 7k=4$

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

$\therefore$ Ratio$=4:7$.