Question

Find the coordinates of the point which divides the line segment joining $(-1,3)$ and $(4,-7)$ internally in the ratio $3:4$.

Answer 1

Required coordinates of the point$=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

Here, $m=3,m=4$, and $x_1=-1,y_1=3,x_2=4,y_2=-7$

$\therefore$ Required points

$=(\frac{3\left(4\right)+4(-1)}{3+4},\frac{3(-7)+4\left(3\right)}{3+4})$

$=(\frac{(12-4)}{7},\frac{(-21+12)}{7})$.

$=(\frac{8}{7},\frac{-9}{7})$.