Question

Question 8
If A and B are (–2, –2) and (2, –4), respectively, find the coordinates of P such that $AP=\frac{3}{7}AB$ and P lies on the line segment AB.

Answer 1

The coordinates of point A and B are (-2,-2) and (2,-4) respectively.
Since $AP=\frac{3}{7}AB$
Therefore, AP:PB = 3:4
Point P divides the line segment AB in the ratio 3:4.
Coordinates of $P=(\frac{3\times 2+4\times (-2)}{3+4},\frac{3\times (-4)+4\times (-2)}{3+4})$
$=(\frac{6-8}{7},\frac{-12-8}{7})$
$=(\frac{-2}{7},\frac{-20}{7})$