Question

Let A(2, 1, -3) and B(5, -8, 3) be two given points. Find the coordinates of the points of trisection of the line segment AB.

Answer 1

Let P and Q be the points trisection of AB. Then, P divides AB in the ratio 1:2 and Q divides AB in the ratio 2:1.

For P

$x=\frac{1\times 5+2\times 2}{1+2}=\frac{9}{3}=3$

$y=\frac{1\times -8+2\times 1}{1+2}=\frac{11}{3}$

$z=\frac{1\times 3+2\times -3}{1+2}=-1$

For Q

$x=\frac{2\times 5+1\times 2}{1+2}=\frac{13}{3}$

$y=\frac{2\times -8+1\times 1}{1+2}=-5$

$z=\frac{2\times 3+1\times -3}{1+2}=1$