At what ratio does the point $(-4,6)$ divide the line segment joining the points A$(-6,10)$ and B$(3,-8)$?

Let’s the point $(-4,6)$ divide the line segment AB in the ratio k:$1$.

Thus, by using the section formula, we have

$(-4,6)=\left( \frac{3k-6}{k+1},\frac{-8k+10}{k+1} \right)$

$-4=\frac{3k-6}{k+1}$

$-4k-4=3k-6$

$7k=2$

$k:1=2:7$

So the same can be checked for the y-coordinate also.

Thus , the ratio in which the point $(-4,6)$ divides the line segment AB is $2:7$