A point P on the segment AB is three times as far from A as it is from B, where A(-4, 6) and B(8, 2).
Find the coordinates of P.

Three times as far from A as from B means AP : PB = 3 : 1. $x=\frac{3\cdot 8+1\cdot (-4)}{4}=\frac{20}{4}=5$ and $y=\frac{3\cdot 2+1\cdot 6}{4}=\frac{12}{4}=3$, so $P$ = (5, 3). (-1, 5) reads the sentence backwards and uses 1 : 3; (2, 4) is the midpoint, which would make the two distances equal; (5, 4) keeps the correct $x$ but takes the plain average of the $y$-values.