The median of a triangle is the line segment that joins a vertex of a triangle to the mi...

The median of a triangle is the line segment that joins a vertex of a triangle to the midpoint of the opposite side. The purpose of this problem is to use vectors to show that the medians of a triangle all meet at a point.

(a) Using Figure 1.113, write the vectors

(b) Let P be the point of intersection of

(c) Use the fact that show that P must lie two-thirds of the way from B to M₁ and two-thirds of the way from C to M₂.

(d) Now use part (c) to show why all three medians must meet at P.