If A and B are points $(-2, -2)$ and $(2, -4)$ and P is a point lying on AB such that AP = $\frac{3}{7}$ AB, then find coordinates of P.
Given: If A and B are points $(-2, -2)$ and $(2, -4)$ and P is a point lying on AB such that AP = $\frac{3}{7}$ AB
To Do: Find coordinates of P.
Answer:
Given A and B are points $(-2, -2)$ and $(2, -4)$. P is a point such that AP = $\frac{3}{7}$ AB or
PB = $\frac{4}{7}$ AB
This means P divides AB in the ratio 3 : 4
The coordinates of point P = $\frac{m\times2 + n\times1}{m + n}$, $\frac{my2 + ny1}{m + n}$
=$\frac{3\times2 + 4\times-2}{3+4}, \frac{3\times-4 + 4\times-2}{3+4}$
= $\frac{6-8}{7}, \frac{-12-8}{7}$
Therefore, the coordinates of P are $\frac{-2}{7}, \frac{-20}{7}$
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