Calc1131W9T4 - Bezier Curves

The triangle ABC has weights placed at the points A,B and C. At A the weight is (1-t)^2 At B the weight is 2t(1-t) At C the weight is t^2. The point r(t) is at the centre of mass of this triangle. This is also the de Castlejau-Bezier curve with control points A,B and C.
Find the centre of mass at t = 0 t=1/2 t = 1