MathDB
1994 AMC 12 #23

Source:

December 30, 2011
analytic geometrygraphing linesslopegeometrytrapezoidAMC

Problem Statement

In the xyxy-plane, consider the L-shaped region bounded by horizontal and vertical segments with vertices at (0,0),(0,3),(3,3),(3,1),(5,1)(0,0), (0,3), (3,3), (3,1), (5,1) and (5,0)(5,0). The slope of the line through the origin that divides the area of this region exactly in half is [asy] size(200); Label l; l.p=fontsize(6); xaxis("xx",0,6,Ticks(l,1.0,0.5),EndArrow); yaxis("yy",0,4,Ticks(l,1.0,0.5),EndArrow); draw((0,3)--(3,3)--(3,1)--(5,1)--(5,0)--(0,0)--cycle,black+linewidth(2));[/asy] <spanclass=latexbold>(A)</span> 27<spanclass=latexbold>(B)</span> 13<spanclass=latexbold>(C)</span> 23<spanclass=latexbold>(D)</span> 34<spanclass=latexbold>(E)</span> 79 <span class='latex-bold'>(A)</span>\ \frac{2}{7} \qquad<span class='latex-bold'>(B)</span>\ \frac{1}{3} \qquad<span class='latex-bold'>(C)</span>\ \frac{2}{3} \qquad<span class='latex-bold'>(D)</span>\ \frac{3}{4} \qquad<span class='latex-bold'>(E)</span>\ \frac{7}{9}