The points of trisection of the line segment | vedclass

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Question

(C) Let $A(3, -2)$ and $B(-3, -4)$ be the endpoints of the line segment,and let $C$ and $D$ be the points of trisection.$C$ divides $AB$ in the ratio

Vedclass · Accepted Answer

$\left( 1, - \frac{8}{3} \right), \left( - 1, - \frac{10}{3} \right)$

Vedclass · Answer

(C) Let $A(3, -2)$ and $B(-3, -4)$ be the endpoints of the line segment,and let $C$ and $D$ be the points of trisection.$C$ divides $AB$ in the ratio $1:2$. Using the section formula,the coordinates of $C$ are:$\left( \frac{1(-3) + 2(3)}{1+2}, \frac{1(-4) + 2(-2)}{1+2} \right) = \left( \frac{3}{3}, \frac{-8}{3} \right) = \left( 1, - \frac{8}{3} \right)$.$D$ divides $AB$ in the ratio $2:1$. Using the section formula,the coordinates of $D$ are:$\left( \frac{2(-3) + 1(3)}{2+1}, \frac{2(-4) + 1(-2)}{2+1} \right) = \left( \frac{-3}{3}, \frac{-10}{3} \right) = \left( -1, - \frac{10}{3} \right)$.

The points of trisection of the line segment joining the points $(3, -2)$ and $(-3, -4)$ are

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