2013 AMC 10A Problem 18

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 \bigg(\frac{p}{q}, \frac{r}{s}\bigg), where these fractions are in lowest terms. What is p+q+r+s?

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

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