The centre of mass of a triangular plate

We present a derivation for the coordinates of the centre of mass-or centre of gravity-of a homogeneous triangular plate by using scaling and symmetry. We scale the triangular plate by a factor of 2 and divide its area into four plates identical to the original. By symmetry, we assert that the centre of mass of two identical masses lies at the midpoint of the line joining their centres of mass. By relating the centres of mass of the original to those of the scaled plates, we find the coordinates of the centre of mass as the solution of an algebraic equation