Question

Find the points of trisection of the line segment joining the points:
$(2,-2)$ and $(-7,4)$

Answer 1

Trisection means dividing a line segment in three equal parts or dividing a line segment in the ratio $1:2$ and $2:1$

CASE :- 1

$m:n=1:2$

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

$=(\frac{1(-7)+2\left(2\right)}{1+2},\frac{1\left(4\right)+2(-2)}{1+2})$

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

$=(-1,0)$

CASE :- 2

$m:n=2:1$

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

$=(\frac{2(-7)+1\left(2\right)}{2+1},\frac{2\left(4\right)+1(-2)}{2+1})$

$=(\frac{-14+2}{3},\frac{8-2}{3})$

$=(\frac{-12}{3},\frac{6}{3})$

$=(-4,2)$