Question

The ratio in which the x-axis divides the line segment joining the points $(6,4)$ and $(1,-7)$ is $m:n$, then $m+n$ =.

Answer 1

Let the line segment joining the points (6,4) and (1,-7) be divided by the point on x-axis(x,0) in the ratio $k:1$.

Using section formula,

$\frac{-7k+4}{k+1}=0$

$-7k+4=0$

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

Therefore, the ratio $m:n$ is $\frac{4}{7}:1⟹4:7$

Hence, $m+n=4+7=11$