Find the co-ordinates of the points of trisection of the line segment joining the points $(3, -1)$ and $(6, 8)$.

[IMAGE_1]

Question

Find the co-ordinates of the points of trisection of the line segment joining the points $(3, -1)$ and $(6, 8)$.

[IMAGE_1]

Accepted Answer

Step 1: Case I: If $C$ and $D$ trisect $AB$, then $C$ divides $AB$ in the ratio $1 : 2$. Co-ordinates of $C$: $x = \frac{1 	imes 6 + 2 	imes 3}{3} = 4$, $y = \frac{1 	imes 8 + 2 	imes (-1)}{3} = 2$. $	herefore C(4, 2)$
Step 2: Case II: $D$ divides $AB$ in the ratio $2 : 1$. Co-ordinates of $D$: $x = \frac{2 	imes 6 + 1 	imes 3}{3} = 5$, $y = \frac{2 	imes 8 + 1 	imes (-1)}{3} = 5$. Coordinates of $D = (5, 5)$

Question

Solution