A point P lies on the segment AB, where A(6, -2) and B(-4, 8), and PB : AB = 1 : 5.
Find the coordinates of P.

PB : AB = 1 : 5 means AP : AB = 4 : 5, and therefore AP : PB = 4 : 1. $x=\frac{4\cdot (-4)+1\cdot 6}{5}=\frac{-16+6}{5}=-2$ and $y=\frac{4\cdot 8+1\cdot (-2)}{5}=\frac{30}{5}=6$, so $P$ = (-2, 6). (4, 0) uses AP : PB = 1 : 4, reading the given ratio the wrong way round; (1, 3) is the midpoint, which would need PB : AB = 1 : 2; (-2, -6) mishandles the sign, treating 32 - 2 as -30.