In triangle ABC the vertex A is (2, 8) and D(5, 2) is the midpoint of BC. Using the fact that the centroid divides the median AD in the ratio 2 : 1 measured from A, find the centroid G.

The **centroid** is the point where the three medians of a triangle meet (a median connects a vertex to the midpoint of the opposite side). It is the 'balance point' of the triangle.

**Coordinates**: just the average of the three vertices:
$G=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$.

**Example**: Triangle with A(0, 0), B(6, 0), C(3, 9).
Centroid: $(\frac{0+6+3}{3},\frac{0+0+9}{3})$ = (3, 3).

A useful invariant — the centroid divides each median in ratio 2:1 from the vertex.