Let \( \triangle ABC \) 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 \( \triangle ABC \) in the line \( 3x+6y-53=0 \). Then \( h^2+k^2+hk \) is equal to:
