# 2016 AMC 10A Problems/Problem 16

## Problem

A triangle with vertices $A(0, 2)$, $B(-3, 2)$, and $C(-3, 0)$ is reflected about the $x$-axis, then the image $\triangle A'B'C'$ is rotated counterclockwise about the origin by $90^{\circ}$ to produce $\triangle A''B''C''$. Which of the following transformations will return $\triangle A''B''C''$ to $\triangle ABC$? $\textbf{(A)}$ counterclockwise rotation about the origin by $90^{\circ}$. $\textbf{(B)}$ clockwise rotation about the origin by $90^{\circ}$. $\textbf{(C)}$ reflection about the $x$-axis $\textbf{(D)}$ reflection about the line $y = x$ $\textbf{(E)}$ reflection about the $y$-axis.

## Solution

Consider a point $(x, y)$. Reflecting it about the $x$-axis will map it to $(x, -y)$, and rotating it counterclockwise about the origin by $90^{\circ}$ will map it to $(y, x)$. The operation that undoes this is a reflection about the $y = x$, so the answer is $\boxed{\textbf{(D)}}$.

## Video Solution 2

~IceMatrix

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