Centroid

1. The centroid of a triangle is the intersection of the three medians of the triangle.

2. A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side.

Experiment with the free-form simulation, of centroid of a triangle, below:

 

Experiment with the above simulation to answer the following Questions.

Q1: Can centroid of a triangle lie/exist outside of the triangle? If yes, when? If no, Why?

Q2: Does centroid of a triangle divide the median in any fixed ratio?

Q3: Is centroid of a triangle average of all points on that triangle? Why?