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# If A and B are (minus 2, minus 2) and (2, minus 4), respectively, find the coordinates of P such that AP = 3 AB 7 and P lies on the line segment AB.

8.   If A and B are (- 2, - 2) and (2, -  4), respectively, find the coordinates of P such that AP = 3 AB 7 and P lies on the line segment AB.

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From the figure:

As $AP = \frac{3}{7}AB$

$\Rightarrow PB = \frac{4}{7}AB$ hence the ratio is  3:4,

Now, from the section formula, we can find the coordinates of Point P.

Section Formula:

$P(x,y)= \left (\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}} , \frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}} \right )$

$P(x,y)= \left (\frac{3(2)+4(-2)}{3+4} , \frac{3(-4)+4(-2)}{3+4} \right )$

$P(x,y)= \left (\frac{6-8}{7} , \frac{-12-8}{7} \right )$

$P(x,y)= \left (\frac{-2}{7} , \frac{-20}{7} \right )$

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