AMC 12 2013a Problem 13

Let points $A = (0,0) , \ B = (1,2), \ C = (3,3),$ and $D = (4,0)$. Quadrilateral $ABCD$ is cut into equal area pieces by a line passing through $A$. This line intersects $\overline{CD}$ at point $\left (\frac{p}{q}, \frac{r}{s} \right )$, where these fractions are in lowest terms. What is $p + q + r + s$?

\textbf{(A)} \ 54 \textbf{(B)} \ 58 \textbf{(C)} \ 62 \textbf{(D)} \ 70 \textbf{(E)} \ 75