2009 AMC 12B Problem 14

Five unit squares are arranged in the coordinate plane as shown, with the lower left corner at the origin. The slanted line, extending from (c,0)(c,0) to (3,3)(3,3) , divides the entire region into two regions of equal area. What is cc ?

[asy] unitsize(0.2cm); defaultpen(linewidth(.8pt)+fontsize(8pt)); fill((2/3,0)--(3,3)--(3,1)--(2,1)--(2,0)--cycle,gray); xaxis("$x$",-0.5,4,EndArrow(HookHead,4)); yaxis("$y$",-0.5,4,EndArrow(4)); draw((0,1)--(3,1)--(3,3)--(2,3)--(2,0)); draw((1,0)--(1,2)--(3,2)); draw((2/3,0)--(3,3)); label("$(c,0)$",(2/3,0),S); label("$(3,3)$",(3,3),NE); [/asy]
(A) 12(B) 35(C) 23(D) 34(E) 45\textbf{(A)}\ \frac12\qquad \textbf{(B)}\ \frac35\qquad \textbf{(C)}\ \frac23\qquad \textbf{(D)}\ \frac34\qquad \textbf{(E)}\ \frac45

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

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Category: AMC 12B
Points: 3
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