Find the coordinates of the points of trisection of the line segment joining the points A$\displaystyle (-1, 4)$ and B$\displaystyle (-3, -2)$.

\[\begin{array}{cccc} \underset{\Gamma}{A} & \mathrm{P} & \mathrm{Q} & \mathrm{~B} \\ (-1,4) & & & (-3,-2) \end{array} \] Let P and Q be the points of trisection of AB , therefore \(\displaystyle \mathrm{AP}: \mathrm{PB}=1: 2\) Coordinates of \(\displaystyle \mathrm{P}=\left(\frac{1(-3)+2(-1)}{3}, \frac{1(-2)+2(4)}{3}\right)\) \(\displaystyle =\left(\frac{-5}{3}, 2\right)\) Q is the mid-point of PB Coordinates of \(\displaystyle \mathrm{Q}=\left(\frac{\dfrac{-5}{3}+(-3)}{2}, \frac{2+(-2)}{2}\right)\) \(\displaystyle =\left(\frac{-7}{3}, 0\right)\)