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(A) True.Let point $P(5, -3)$ divide the line segment joining $A(7, -2)$ and $B(1, -5)$ in the ratio $k: 1$ internally.By the section formula,the coor

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(A) True.Let point $P(5, -3)$ divide the line segment joining $A(7, -2)$ and $B(1, -5)$ in the ratio $k: 1$ internally.By the section formula,the coordinates of point $P$ are given by:$\left( \frac{k(1) + 1(7)}{k + 1}, \frac{k(-5) + 1(-2)}{k + 1} \right) = \left( \frac{k + 7}{k + 1}, \frac{-5k - 2}{k + 1} \right)$.Equating these to the given coordinates of $P(5, -3)$:$\frac{k + 7}{k + 1} = 5 \implies k + 7 = 5k + 5 \implies 2 = 4k \implies k = \frac{1}{2}$.Checking the $y$-coordinate with $k = \frac{1}{2}$:$\frac{-5(1/2) - 2}{1/2 + 1} = \frac{-2.5 - 2}{1.5} = \frac{-4.5}{1.5} = -3$.Since the ratio is $1: 2$,point $P$ divides the segment $AB$ such that it is one of the two points of trisection (the other being at ratio $2: 1$). Thus,the statement is true.

State whether the following statement is true or false. Justify your answer.
Point $P(5, -3)$ is one of the two points of trisection of the line segment joining the points $A(7, -2)$ and $B(1, -5)$.

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State whether the following statement is true or false. Justify your answer.Point $P(5, -3)$ is one of the two points of trisection of the line segment joining the points $A(7, -2)$ and $B(1, -5)$.