MathDB
Triangle

Source: 2016 AMC 10A #16

February 3, 2016
AMCAMC 10AMC 10 Arotation

Problem Statement

A triangle with vertices A(0,2)A(0, 2), B(3,2)B(-3, 2), and C(3,0)C(-3, 0) is reflected about the xx-axis, then the image ABC\triangle A'B'C' is rotated counterclockwise about the origin by 9090^{\circ} to produce ABC\triangle A''B''C''. Which of the following transformations will return ABC\triangle A''B''C'' to ABC\triangle ABC?
<spanclass=latexbold>(A)</span><span class='latex-bold'>(A)</span> counterclockwise rotation about the origin by 9090^{\circ}. <spanclass=latexbold>(B)</span><span class='latex-bold'>(B)</span> clockwise rotation about the origin by 9090^{\circ}. <spanclass=latexbold>(C)</span><span class='latex-bold'>(C)</span> reflection about the xx-axis <spanclass=latexbold>(D)</span><span class='latex-bold'>(D)</span> reflection about the line y=xy = x <spanclass=latexbold>(E)</span><span class='latex-bold'>(E)</span> reflection about the yy-axis.