9.1 Introduction and Review of Coordinate Geometry

The centroid divides the median in the ratio 2:1. Let $D$ be the midpoint of $BC$. Coordinates of $D = (\frac{x_2+x_3}{2}, \frac{y_2+y_3}{2})$. Let $G$ be the centroid on median $AD$ such that $AG:GD = 2:1$. Using Section Formula: $x_G = \frac{2(\frac{x_2+x_3}{2}) + 1(x_1)}{2+1} = \frac{x_1+x_2+x_3}{3}$ $y_G = \frac{y_1+y_2+y_3}{3}$