Medians of a Trianlge in Vector Space

by Venessa Brown

The goal of this assignment is to prove that meadians of a triangle is are concurrent and the they meet at a point 2/3 of the way from the vertex to the midpoint of the opposite side.

Prove that the medians of a triangle are concurrent:

Looking at the figure it appears that the medians meet at 2/3 of the way ( will be proved later). Will use this hunch to show that all the medians meet at a common point.

The medians do infact meet at a point 1/3 (u + v + w)

Prove that the centroid is 2/3 the distance from a vertex to the midpoint of the opposite side.

Let z be the point of concurrency. Then: