AMC 12 2009b 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 $(c,0)$ to $(3,3)$, divides the entire region into two regions of equal area. What is $c$?

unitsize(1cm);
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);

\textbf{(A)}\ \frac12 \textbf{(B)}\ \frac35 \textbf{(C)}\ \frac23 \textbf{(D)}\ \frac34 \textbf{(E)}\ \frac45