Chapter 13.6, Problem 64E

Triangle medians A triangular region has a base that connects the vertices (0, 0) and (b, 0), and a third vertex at (a, h), where a > 0, b > 0, and h > 0.

  a.    Show that the centroid of the triangle is $\left(\frac{a+b}{3},\frac{h}{3}\right)$.

b.    Recall that the three medians of a triangle extend from each vertex to the midpoint of the opposite side. Knowing that the medians of a triangle intersect in a point M and that each median bisects the triangle, conclude that the centroid of the triangle is M.