What are the coordinates of the points of tri | vedclass

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Question

(A) Let the points be $P(-3, -3)$ and $Q(6, 6)$.Let $R$ and $S$ be the points of trisection.$R$ divides $PQ$ in the ratio $1:2$.Using the section form

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$(0, 0), (3, 3)$

Vedclass · Answer

(A) Let the points be $P(-3, -3)$ and $Q(6, 6)$.Let $R$ and $S$ be the points of trisection.$R$ divides $PQ$ in the ratio $1:2$.Using the section formula,the coordinates of $R$ are:$R = \left( \frac{1(6) + 2(-3)}{1+2}, \frac{1(6) + 2(-3)}{1+2} \right) = \left( \frac{6-6}{3}, \frac{6-6}{3} \right) = (0, 0)$.$S$ divides $PQ$ in the ratio $2:1$.Using the section formula,the coordinates of $S$ are:$S = \left( \frac{2(6) + 1(-3)}{2+1}, \frac{2(6) + 1(-3)}{2+1} \right) = \left( \frac{12-3}{3}, \frac{12-3}{3} \right) = \left( \frac{9}{3}, \frac{9}{3} \right) = (3, 3)$.Thus,the coordinates of the points of trisection are $(0, 0)$ and $(3, 3)$.

What are the coordinates of the points of trisection of the line segment joining the points $(-3, -3)$ and $(6, 6)$?

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