Question

Find the coordinates of point P which divides the line joining $A(4,-5)$ and $B(6,3)$ in the ratio $2:5$.

Answer 1

Let the coordinates of P be (x, y). Given $m:n=2:5$
$(x_1,y_1)=(4,-5)$ and $(x_2,y_2)=(6,3)$
by section formula,
$x=\frac{m{x}_2+n{x}_1}{m+n}=\frac{2\left(6\right)+5\left(4\right)}{2+5}=\frac{12+20}{7}=\frac{32}{7}$
$y=\frac{m{y}_2+m{y}_1}{m+n}=\frac{2\left(3\right)+5(-5)}{2+\left(5\right)}=\frac{6-25}{7}=\frac{-19}{7}$
$\therefore$ Coordinates of $P=\left(\frac{32}{7},\frac{-19}{7}\right)$