(a) Let the vertices of and C (3, 1). Find the point on each median that is two-thirds...

(a) Let the vertices of and C (3, 1). Find the point on each median that is two-thirds of the way from the vertex to the midpoint of the opposite side. (Recall that a median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side.) What do you observe?

Hint: Use the result in Exercise 88.

(b) Follow part (a) but take the vertices to be A(0, 0), B(2a, 0), and C(2b, 2c). What do you observe? What does this prove?