The medial triangle of a triangle ABC is the triangle whose vertices are located at the midpoints of the sides AB, AC, and BC of triangle ABC. From an arbitrary point O that is not a vertex of triangle ABC, you may take it as a given fact that the locatio

Scenario:

The medial triangle of a triangle ABC is the triangle whose vertices are located at the midpoints of the sides AB, AC, and BC of triangle ABC. From an arbitrary point O that is not a vertex of triangle ABC, you may take it as a given fact that the location of the centroid of triangle ABC is the vector (vector OA + vector OB + vector OC)/3.

Task:

A. Use vector techniques to prove that a triangle and its medial triangle have the same centroid, stating each step of the proof.
1. Provide written justification for each step of your proof.

B. Provide a convincing argument short of a proof (suggested length of 3–4 sentences) that the theorem is true.

Additional Requirements

Level of Detail: Show all work
Other Requirements: -Arbitrary point O should be outside of the triangle
-Needs illustration for part A ( you can hand draw if that easier)
-The main idea in part B is to convince someone that the theorem is true. You do not have to use vector techniques. can use ratio's or coordinated, or any other technique.