Question

Find the coordinates of the points which divides initially the join of the points.
$\left(a\right)(8,9)$ and $(-7,4)$ in the ratio $2:3;$
$\left(b\right)(1,-2)$ and $(4,7)$ in the ratio $1:2$

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

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

(a) Points are $(8,9)$ and $(-7,4)$

Also, $m:n=2:3$

Therefore, we have

$(x,y)=(\frac{8\times 3-7\times 2}{5},\frac{9\times 3+4\times 2}{5})$

$=(\frac{24-14}{5},\frac{27+8}{5})$

$=(2,7)$

(b) Points are $(1,-2)$ and $(4,7)$

Also, $m:n=1:2$

Therefore, we have

$(x,y)=(\frac{1\times 2+4\times 1}{1+2},\frac{-2\times 2+7\times 1}{1+2})$

$=(2,1)$