I recently started studying Mass Points and the question arose:
If you have a quadrilateral with a mass of 1 at each vertex, how do you locate the center of mass.
I had several approaches but I was not sure if they all result in the same point or not. My approaches are:
With quadrilateral ABCD, find the center of mass of triangle ABC, which will have weight 3, and the center of mass of the quadrilateral will be 1/4 of the way into the segment from the centroid of ABC to point D.
Connect the centroids of ABC and BCD and the centroids of ABD and ACD. The intersection will be the center of mass of ABCD.
Connect the midpoints of AB and CD and the midpoints of BC and AD. The intersection will be the center of mass of ABCD.
Are these three points the same?