Functions - Linear Function

SOURCE:COMPETITION
Number of Problems: 1. : (Book)

1.

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

$extbf{(A)} 54qquad extbf{(B)} 58qquad extbf{(C)} 62qquad extbf{(D)} 70qquad extbf{(E)} 75$

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