The line segment joining the points $A(4, -5)$ and $B(4, 5)$ is divided by the point $P$ such that $AP : AB = 2 : 5$. Find the coordinates of $P$.

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Accepted Answer

Step 1: $AP : AB = 2 : 5 \Rightarrow AP : PB = 2 : 3$
Step 2: Using section formula with ratio $2 : 3$:
$x = \frac{2 	imes 4 + 3 	imes 4}{5} = 4$, $y = \frac{2 	imes 5 + 3 	imes (-5)}{5} = \frac{10 - 15}{5} = -1$
Step 3: Point $P$ is $(4, -1)$

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