Question

Show that $A(3,-2)$ is a point trisection of the line segment joining the points $(2,1)$ and $(5,-8)$
Also find the co-ordinates of the other points of trisections.

Answer 1

R.E.F image

$T_1$diudes AB in 1:2 ratio

$\therefore$ $T_1\{\frac{5+2\times 2}{3},\frac{1\times 2-8\times 1}{3}\}$

$\left[T_1\right(3,-2\left)\right]$ proved

$T_2$ duides AB in 2:1 ratio

$\therefore$ $T_2\{\frac{5\times 2+2}{3},\frac{-8\times 2+1}{3}\}$

$\left[T_2\right(4,-5\left)\right]$