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Perpendicular lines

Source: AHSME 1963 Problem 7

January 9, 2014
analytic geometrygraphing linesslopeAMC

Problem Statement

Given the four equations:
<spanclass=latexbold>(1)</span> 3y2x=12<spanclass=latexbold>(2)</span> 2x3y=10<spanclass=latexbold>(3)</span> 3y+2x=12<spanclass=latexbold>(4)</span> 2y+3x=10<span class='latex-bold'>(1)</span>\ 3y-2x=12 \qquad <span class='latex-bold'>(2)</span>\ -2x-3y=10 \qquad <span class='latex-bold'>(3)</span>\ 3y+2x=12 \qquad <span class='latex-bold'>(4)</span>\ 2y+3x=10
The pair representing the perpendicular lines is:
<spanclass=latexbold>(A)</span> (1) and (4)<spanclass=latexbold>(B)</span> (1) and (3)<spanclass=latexbold>(C)</span> (1) and (2)<spanclass=latexbold>(D)</span> (2) and (4)<spanclass=latexbold>(E)</span> (2) and (3)<span class='latex-bold'>(A)</span>\ \text{(1) and (4)} \qquad <span class='latex-bold'>(B)</span>\ \text{(1) and (3)} \qquad <span class='latex-bold'>(C)</span>\ \text{(1) and (2)} \qquad <span class='latex-bold'>(D)</span>\ \text{(2) and (4)} \qquad <span class='latex-bold'>(E)</span>\ \text{(2) and (3)}