We have
12x2 - 20xy + 7y2 ≡(2x - y)(6x - 7y)
Therefore, the sides of the triangle are
2x - y = 0 ......(1)
6x - 7y = 0 .....(2)
2x - 3y = -4 ......(3)
Solving Eqs. (1) and (2), we get (1,2) as the vertex. Solving Eqs. (2) and (3), we obtain (7, 6) as another vertex.By hypotheses, (0, 0) is the third vertex. Hence, the centroid of the triangle is
(0 + 1 + 7/3 , 0 + 2 + 6/3) = (8/3,8/3)