Problem Statement
Find the coordinates of the points of trisection of the line segment joining $A(2, -2)$ and $B(-7, 4)$.
Verified Solution & Marking Scheme
Define Trisection Points P and Q
Points of trisection $P$ and $Q$ divide $AB$ in ratios $1 : 2$ and $2 : 1$ respectively.
Find Coordinates of P (Ratio 1 : 2)
$x_P = \frac{1(-7) + 2(2)}{1 + 2} = \frac{-7 + 4}{3} = \frac{-3}{3} = -1$
$y_P = \frac{1(4) + 2(-2)}{1 + 2} = \frac{4 - 4}{3} = 0$
So $P = (-1, 0)$.
Find Coordinates of Q (Midpoint of PB or Ratio 2 : 1)
$x_Q = \frac{2(-7) + 1(2)}{2 + 1} = \frac{-14 + 2}{3} = \frac{-12}{3} = -4$
$y_Q = \frac{2(4) + 1(-2)}{2 + 1} = \frac{8 - 2}{3} = \frac{6}{3} = 2$
So $Q = (-4, 2)$.