Question

Show that the coordinates of the point which divides the line segment joining the points $(a+b,a-b)$ and $(a-b,a+b)$ in the ratio $3:2$ are $(\frac{5a+b}{5},\frac{5a-b}{5})$

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

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

Let point $P$ be the required point.

Using section formula, we get

$P=(\frac{3(a+b)+2(a-b)}{3+2},\frac{3(a-b)+2(a+b)}{3+2})$

$P=(\frac{5a+b}{5},\frac{5a-b}{5})$

Hence proved.