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 $AB$.

(N/A) The coordinates of points $A$ and $B$ are $(-2, -2)$ and $(2, -4)$ respectively.
Since $AP = \frac{3}{7} AB$,it implies that $AP : AB = 3 : 7$.
Therefore,$AP : PB = 3 : (7 - 3) = 3 : 4$.
Point $P$ divides the line segment $AB$ in the ratio $m : n = 3 : 4$.
Using the section formula,the coordinates of $P$ are given by:
$P = \left( \frac{mx_2 + nx_1}{m + n}, \frac{my_2 + ny_1}{m + n} \right)$
$P = \left( \frac{3(2) + 4(-2)}{3 + 4}, \frac{3(-4) + 4(-2)}{3 + 4} \right)$
$P = \left( \frac{6 - 8}{7}, \frac{-12 - 8}{7} \right)$
$P = \left( -\frac{2}{7}, -\frac{20}{7} \right)$