Find the coordinates of the points of trisection of the line segment joining the points P (5, -4) and Q (-4, 2) .

Let the points A and B trisect the line segment joining P and Q.
$\therefore$ PA : AQ = $1:2$. (1 Mark)
Coordinates of A = $(\frac{1 \times (-4) + 2 \times 5}{1+2}, \frac{1 \times 2 + 2 \times (-4)}{1+2})$ ($\frac{1}{2}$ Mark)
$= (2, -2)$ ($\frac{1}{2}$ Mark)
Now, B is mid point of the line segment joining A and Q.
Coordinates of B = $(\frac{2 - 4}{2}, \frac{-2 + 2}{2})$ ($\frac{1}{2}$ Mark)
$= (-1, 0)$ ($\frac{1}{2}$ Mark)
The line segment joining P and Q is trisected at $(2, -2)$ and $(-1, 0)$.