Question

Find the coordinates of the points of trisection of line segment joining the points $(- 4, 1)$ and $(6, 5)$ .

Approach

Let $P$ divide $A B$ in ratio $1 : 2$ and $Q$ in ratio $2 : 1$ . Using section formula, $P = (\frac{- 8 + 6}{3}, \frac{5 + 2}{3}) = (- \frac{2}{3}, \frac{7}{3})$ and $Q = (\frac{12 - 4}{3}, \frac{10 + 1}{3}) = (\frac{8}{3}, \frac{11}{3})$ .

Step-by-step working

1
For $A P : PB = 1 : 2$ , $P = (\frac{- 2}{3}, \frac{7}{3})$
1 mark
2
For $A Q : QB = 2 : 1$ , $Q = (\frac{8}{3}, \frac{11}{3})$
1 mark

Concepts used

section formulatrisectioncoordinatesline segment

Approach

Step-by-step working

Concepts used

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