Question

Find the points of trisection of the line joining the points:
$(5,-6)$ and $(-7,5)$

Answer 1

Trisection means dividing a time segment in three equal parts or dividing a time segment in the ratio 1:2 and 2:1 internally.

CASE :- 1

$m:n=1:2$

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

$=(\frac{-7+10}{3},\frac{5-12}{3})$

$=(1,\frac{-7}{3})$

CASE :- 2

$m:n=2:1$

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

$=(\frac{2(-7)+1\left(5\right)}{2+1},\frac{2\left(5\right)+1(-6)}{2+1})$

$=(\frac{-14+5}{3},\frac{10-6}{3})$

$=(\frac{-9}{3},\frac{4}{3})$

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