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Baricenter of a triangle


Note the triangle in the following figure, where M, N and P are the midpoints of the sides respectively. Therefore, are the medians of this triangle:

We call it baricenter (G) the intersection point of the medians of a triangle. This point divides the median relative to one side into two parts: the one from the vertex to the baricenter is twice the median from the one from the baricenter to the midpoint of the side. Look:

Calculation of baricenter coordinates

Being THE(XTHE, YTHE), B(XB, YB) and Ç(XÇ, YÇ) vertices of a triangle if N is midpoint of we have:

But:

Similarly, we determine . Like this:

Next: Three Point Alignment Conditions