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 $\Delta$ABC in the line $3x + 6y - 53 = 0$. Then ${h^2} + {k^2} + hk$ is equal to :
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