Explored by:
Aubrey D. Johnson
A centroid is a point whose coordinates are the averages of the corresponding coordinates of a given set of points and which for a given plane or three-dimensional figure (as a triangle or sphere) corresponds to the center of mass of a thin plate of uniform thickness and consistency or a body of uniform consistency having the same boundary (according to Webster.com).
The three triangles above, are not to scale, but represent types of triangles. The centroid in each is yellow. I created the centroid by creating a midpoint on each edge. I then connected the midpoint to the vertex across from it, this line is colored hot pink. The intersection of the three pink lines is the centroid.