Prove that the centroid of any triangle is located at the point of intersection of the medians. [Hints: Place the axes so that the vertices are (a, 0), (0, b), and (c, 0). Recall that a median is a line segment from a vertex to the midpoint of the opposite side. Recall also that the medians intersect at a point two thirds of the way from each vertex (along the median) to the opposite side.]