Image of Triangle Centroid in Line

Let ABC be a triangle formed by the lines 7x – 6y + 3 = 0, x + 2y –31 = 0 and 9x –2y–19 = 0, Let the point (h,k) be the image of the centroid of ΔABC in the line 3x + 6y –53 = 0. Then h² + k² + hk is equal to