Mass Point Geometry

Mass point geometry is the process of systematically assigning 'weights' to points, which can then be used to deduce lengths, using the fact that the lengths must be inversly proportional to their weight (just like a balanced lever). Additionally, the point dividing the line has a mass equal to the sum of the weights on either end of the line (like the fulcrom of a lever).

For instance, a triangle ABC with it's three medians drawn, with the intersection points being D, E, F, corresponding to AB, BC, and AC respectively. Thus, if we label point A with a weight of 1, B must also have a weight of 1 since A and B are equidistant to D. By the same process, we find C must also have a weight of 1. Now, since A and B both have a weight of 1, D must have a weight of 2 (as is true for E and F). Thus, if we label the centroid P, we can deduce that DP:PC is 1:2 - the inverse ratio of their weights.