Question

If $A$ and $B$ are $(-2,-2),(2,-4)$ Find $P$ such that $AP=\frac{3}{7}AB$

Answer 1

$AP=\frac{3}{7}AB$

$AP=\frac{3}{7}[AP+PB]$

$AP=\frac{3AP+3PB}{7}$

$7AP-3AP=3PB$

or $4AP=3PB$

or $\frac{AP}{PB}=\frac{3}{4}$ ..........$\left(1\right)$

$[m=3,n=4]$

We know

$\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n}$

$\frac{3\left(2\right)+4(-2)}{3+4},\frac{3(-4)+4(-2)}{3+4}$

$(\frac{6-8}{7},\frac{-12-8}{7})$

$\Rightarrow (\frac{2}{7},-\frac{20}{7})$.