2017 AMC 10B Problem 8

Points A(11, 9) and B(2, -3) are vertices of \triangle ABC with AB=AC. The altitude from A meets the opposite side at D(-1, 3). What are the coordinates of point C?

\textbf{(A)}\ (-8, 9)\qquad\textbf{(B)}\ (-4, 8)\qquad\textbf{(C)}\ (-4, 9)\qquad\textbf{(D)}\ (-2, 3)\qquad\textbf{(E)}\ (-1, 0)

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.