Find the coordinates of the points of trisection P and Q of the line-segment AB as shown in the given figure.

Solution: (b) P divides AB in $1 : 2$
Coordinates of P are $\left( \frac{1 \times 4 + 2 \times (-1)}{1+2} , \frac{1 \times 8 + 2 \times 1}{1+2} \right) = \left( \frac{2}{3}, \frac{10}{3} \right)$ (1/2+1/2 Mark)
Q divides AB in $2: 1$
Coordinates of Q are $\left( \frac{2 \times 4 + 1 \times (-1)}{1+2} , \frac{2 \times 8 + 1 \times 1}{1+2} \right) = \left( \frac{7}{3}, \frac{17}{3} \right)$ (1/2+1/2 Mark)