Question

In what ratio does the point $(a,6)$ divide the join of $(-4,3)$ and $(2,8)$?
Also, find the value of $a$.

Answer 1

$6=\frac{8m+3n}{m+n}$

$6m+6n=8n+3n$

$2m=3n$

$\frac{m}{n}=\frac{3}{2}$

$a=\frac{2m-4n}{m+n}=\frac{-8+6}{5}=\frac{-2}{5}$