Find the points of trisection of the line seg | vedclass

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Question

(A) Let the points be $A(7, 5)$ and $B(-2, -1)$. Let the points of trisection be $P$ and $Q$.Point $P$ divides $AB$ in the ratio $1:2$. Using the sect

Vedclass · Accepted Answer

$(4, 3)$ and $(1, 1)$

Vedclass · Answer

(A) Let the points be $A(7, 5)$ and $B(-2, -1)$. Let the points of trisection be $P$ and $Q$.Point $P$ divides $AB$ in the ratio $1:2$. Using the section formula,$P = \left( \frac{1(-2) + 2(7)}{1+2}, \frac{1(-1) + 2(5)}{1+2} \right) = \left( \frac{-2+14}{3}, \frac{-1+10}{3} \right) = \left( \frac{12}{3}, \frac{9}{3} \right) = (4, 3)$.Point $Q$ divides $AB$ in the ratio $2:1$. Using the section formula,$Q = \left( \frac{2(-2) + 1(7)}{2+1}, \frac{2(-1) + 1(5)}{2+1} \right) = \left( \frac{-4+7}{3}, \frac{-2+5}{3} \right) = \left( \frac{3}{3}, \frac{3}{3} \right) = (1, 1)$.Thus,the points of trisection are $(4, 3)$ and $(1, 1)$.

Find the points of trisection of the line segment joining $(7, 5)$ and $(-2, -1)$.

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