MathDB
1996 AJHSME Problem 17

Source:

July 10, 2011
analytic geometrygeometryAMC

Problem Statement

Figure OPQROPQR is a square. Point OO is the origin, and point QQ has coordinates (2,2)(2,2). What are the coordinates for TT so that the area of triangle PQTPQT equals the area of square OPQROPQR?
[asy] pair O,P,Q,R,T; O = (0,0); P = (2,0); Q = (2,2); R = (0,2); T = (-4,0); draw((-5,0)--(3,0)); draw((0,-1)--(0,3)); draw(P--Q--R); draw((-0.2,-0.8)--(0,-1)--(0.2,-0.8)); draw((-0.2,2.8)--(0,3)--(0.2,2.8)); draw((-4.8,-0.2)--(-5,0)--(-4.8,0.2)); draw((2.8,-0.2)--(3,0)--(2.8,0.2)); draw(Q--T);
label("OO",O,SW); label("PP",P,S); label("QQ",Q,NE); label("RR",R,W); label("TT",T,S); [/asy]
NOT TO SCALE
(A) (6,0)(B) (4,0)(C) (2,0)(D) (2,0)(E) (4,0)\text{(A)}\ (-6,0) \qquad \text{(B)}\ (-4,0) \qquad \text{(C)}\ (-2,0) \qquad \text{(D)}\ (2,0) \qquad \text{(E)}\ (4,0)