Problem 64

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Problem 64: (2013 AMC 10a, 18; 2013 AMC12a 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 $\bigg(\frac{p}{q}, \frac{r}{s}\bigg)$, where these fractions are in lowest terms. What is $p+q+r+s$? $\textbf{(A)}\ 54\qquad$ $\textbf{(B)}\ 58\qquad$ $\textbf{(C)}\ 62\qquad$ $\textbf{(D)}\ 70\qquad$ $\textbf{(E)}\ 75$

Solution

Exercise 64: Solution

Let points $A=(0,0)$, $B=(2,3)$, $C=(6,4)$, and $D=(7,0)$. Quadrilateral $ABCD$ is cut into equal area pieces by a line passing through $A$. This line intersects $\overline{CD}$ at point $\left(\frac pq,\frac rs\right)$, where these fractions are in lowest terms. What is $p+q+r+s$?

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