The points of trisection of the line segment | vedclass

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Question

(D) Let the points be $A(0, 3)$ and $B(6, -3)$. The points of trisection $C$ and $D$ divide the line segment $AB$ in the ratio $1:2$ and $2:1$ respect

Vedclass · Accepted Answer

$(2, 1)$ and $(4, -1)$

Vedclass · Answer

(D) Let the points be $A(0, 3)$ and $B(6, -3)$. The points of trisection $C$ and $D$ divide the line segment $AB$ in the ratio $1:2$ and $2:1$ respectively.Using the section formula,the coordinates of $C$ are:$C = \left( \frac{1 	imes 6 + 2 	imes 0}{1 + 2}, \frac{1 	imes (-3) + 2 	imes 3}{1 + 2} ight) = \left( \frac{6}{3}, \frac{3}{3} ight) = (2, 1)$The coordinates of $D$ are:$D = \left( \frac{2 	imes 6 + 1 	imes 0}{2 + 1}, \frac{2 	imes (-3) + 1 	imes 3}{2 + 1} ight) = \left( \frac{12}{3}, \frac{-3}{3} ight) = (4, -1)$Thus,the points of trisection are $(2, 1)$ and $(4, -1)$.

The points of trisection of the line segment joining the points $(0, 3)$ and $(6, -3)$ are:

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