# The endpoints of AB are A (-4,8) and B (12,-4). How do you find the coordinates of P if P lies on AB and is 3/8 the distance from A to B?

$\left(\setminus \frac{4}{11} , \setminus \frac{52}{11}\right)$

#### Explanation:

Assuming the point $P$ lies on the line AB such that

$P A : P B = 3 : 8 \setminus \equiv m : n$

point $P$ internally divides the line AB with end points $A \left(- 4 , 8\right) \setminus \equiv \left({x}_{1} , {y}_{1}\right)$ & $B \left(12 , - 4\right) \setminus \equiv \left({x}_{2} , {y}_{2}\right)$.

The coordinates of point $P$ are given by internal division formula as follows

$\left(\setminus \frac{m {x}_{2} + n {x}_{1}}{m + n} , \setminus \frac{m {y}_{2} + n {y}_{1}}{m + n}\right)$

$\setminus \equiv \left(\setminus \frac{3 \setminus \cdot 12 + 8 \left(- 4\right)}{3 + 8} , \setminus \frac{3 \left(- 4\right) + 8 \left(8\right)}{3 + 8}\right)$

$\setminus \equiv \left(\setminus \frac{4}{11} , \setminus \frac{52}{11}\right)$