Question

Find the coordinates of the points of trisection of the line segment joining $(1,-2)$ and $(-3,4)$.

Answer 1

We know that by section formula, the co-ordinates of the points which divide internally the line segment joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$ is

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

Let $(x_1,y_1)=(1,-2)$ and $(x_2,y_2)=(-3,4)$

The ratios of trisection willbe $1:2$ and $2:1$

$\therefore$ Points of trisection is $(\frac{2x_1+x_2}{3},\frac{2y_1+y_2}{3})$,$(\frac{x_1+2x_2}{3},\frac{y_1+2y_2}{3})$

$⟹(\frac{-1}{3},0),(\frac{-5}{3},2)$