Question
If A and B are two points having coordinates (-2, -2) and (2, -4) respectively, find the coordinates of P such that $\text{AP}=\frac{3}{7}\text{AB}.$
✓
Answer
The coordinates of point A and B are (-2, -2) and (2, -4) respectively.Since, $\text{AP}=\frac{3}{7}\text{AB}$
Therefore, AP : PB = 3 : 4
So, point P divides the line segment AB in a ratio 3 : 4.
Coordinates of $\text{P}=\Big(\frac{3\times2+4\times(-2)}{3+4},\frac{3\times(-4)+4\times(-2)}{3+4}\Big)$
$=\Big(\frac{6-8}{7},\frac{-12-8}{7}\Big)$
$=\Big(\frac{-2}{7},\frac{-20}{7}\Big)$
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