Question

If point (-4,6) divides the line seqment AB with A (-6,10) & B (r,s) in the ratio 2 : 1, then find $r$ and $s$.

Answer 1

Using the section formula, if a point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$, then

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

& for mid points we have, $m:n=1:1$.

Therefore, we have

$(-4,6)=(\frac{2r-6}{2+1},\frac{25+10}{2+1})$

$\Rightarrow \frac{2r-6}{3}=-4$

$\frac{25+10}{3}=6$

$\Rightarrow 2r-6=-12,25+10=18$

$\Rightarrow 2r=-12+6,2s=18-10$

$\Rightarrow 2r=-6,2s=8$

$\therefore r=-3,s=4$