AMC 12 2009b 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 \textbf{(B)}\ \frac23 \textbf{(C)}\ \frac34 \textbf{(D)}\ \frac79 \textbf{(E)}\ \frac78