2009 AMC 12B Problem 23

A region S in the complex plane is defined by S = \{x + iy: - 1\le x\le1, - 1\le y\le1\}. A complex number z = x + iy is chosen uniformly at random from S. What is the probability that \left(\frac34 + \frac34i\right)z is also in S?

\textbf{(A)}\ \frac12\qquad \textbf{(B)}\ \frac23\qquad \textbf{(C)}\ \frac34\qquad \textbf{(D)}\ \frac79\qquad \textbf{(E)}\ \frac78

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