A plane meets the co-ordinate axes at the points \(A, B, C\) respectively in such a way that the centroid of \(\triangle A B C\) is \(\left(1, r, r^{2}\right)\) for some real \(r\). If the plane passes through the point \((5,5,-12)\) then \(r=\)
(A) \(\frac{3}{2}\)
(B) 4
(C) \(-4\)
(D) \(-\frac{3}{2}\)
Ans: \((A, C)\)