As the professor mentioned in lecture, (x,y) is the centroid of the triangle. As a thought exercise, it's interesting to think of an alternate system where $\alpha$=$\beta$=$\gamma$=$\frac{1}{3}$ instead provides an orthocenter, circumcenter, or incenter.

As the professor mentioned in lecture, (x,y) is the centroid of the triangle. As a thought exercise, it's interesting to think of an alternate system where $\alpha$=$\beta$=$\gamma$=$\frac{1}{3}$ instead provides an orthocenter, circumcenter, or incenter.