Centroid of a triangle

What is a centroid?

The point through which all the mass of a triangular bowl seems to act is called the centroid. 

In the diagram above, the medians of the triangle are shown.

The following points are facts about centroid.

1)The centroid is consistently inside the triangle.

2)Each median divides the triangle into two triangles of same area.

3)The centroid is absolutely two-thirds the way forth each median. 

Centroid formula of a triangle:

A centroid of a triangle is the point where the medians of the triangle intersect. If the three vertices are a = [x_a, y_a], b = [x_b, y_b] and c= [x_c, y_c] then the centroid is given by

      C = (1 / 3) (a + b + c)

 

                            C = ((1 / 3) (x_a + x_b + x_c), (1 / 3) (y_a + y_b + y_c))