A triangle has vertices A(-2, 4), B(6, 0) and C(2, 8). E is the midpoint of AB.
The centroid G lies on CE with CG : GE = 2 : 1. Find G.

$E$ = midpoint of AB = $(\frac{-2+6}{2},\frac{4+0}{2})=(2,2).G$ divides CE from C(2, 8) in the ratio 2 : 1: $x=\frac{2\cdot 2+1\cdot 2}{3}=2$ and $y=\frac{2\cdot 2+1\cdot 8}{3}=\frac{12}{3}=4$, so $G$ = (2, 4). This agrees with the centroid formula $(\frac{-2+6+2}{3},\frac{4+0+8}{3})=$ (2, 4). (2, 6) applies the ratio as 1 : 2; (2, 5) treats $G$ as the midpoint of CE; (2, 2) stops at $E$ and never divides CE at all.