2015 Gauss 8 Problem 20

A rectangle has side lengths 3 and 4. One of its vertices is at the point (1,2). Which of the following *could not* be the coordinates of one of its other vertices?

\textbf{(A)}\ (-3,-1)\quad \textbf{(B)}\ (1,-5)\quad \textbf{(C)}\ (5,-1)\quad \textbf{(D)}\ (-2,6)\quad \textbf{(E)}\ (1,-1)

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.