Question

Find the coordinates of the point, which divides the join of $(-1,7)$ and $(4,-3)$ in the ratio $2:3$

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 the co-ordinates of the point be $(x,y)$ which divides the given points in the ratio $2:3$

$x=\frac{3(-1)+2\left(4\right)}{2+3}$ and $y=\frac{3\left(7\right)+2(-3)}{2+3}$]

$\Rightarrow x=\frac{5}{5}$ and $y=\frac{15}{5}$

$\Rightarrow x=1$ and $y=3$

$\therefore$ the point is $(1,3)$