<p><span style="font-size:18px;"><a href="https://www.gregmat.com/quizzes/quiz/prepswift-reflections-across-lines">Reflections Across Lines Exercise</a></span></p><p>In a previous mountain entry, we discussed reflections about the $x$-axis, the $y$-axis, and the origin. But what about <span style="color:#27ae60;">Reflections Across Lines</span>?</p>
<p><strong><span style="color:#8e44ad;">Reflection about the $y=x$ line</span></strong></p>
<ul>
<li>Simply swap the coordinates. For example, the reflection of $(2,4)$ about the line $y=x$ is $(4,2)$</li>
</ul>
<p><strong><span style="color:#8e44ad;">Reflection about the $y=-x$ line</span></strong></p>
<ul>
<li>Swap the coordinates and give the opposite sign to each. For example, the reflection of $(-3, 2)$ about the line $y=-x$ is $(-2, 3)$</li>
</ul>
<p><strong>(Optional)<span style="color:#8e44ad;"> Reflection about a $y = k$ line, where $k$ is a constant</span></strong></p>
<ul>
<li>Keep the $x$-coordinate the same. The $y$-coordinate is $(2k-y)$.</li>
</ul>
<p><strong>(Optional)<span style="color:#8e44ad;"> Reflection about a $x = k$ line, where $k$ is a constant</span></strong></p>
<ul>
<li>Keep the $y$-coordinate the same. The $x$-coordinate is $(2k-x)$.</li>
</ul>
<p>See why I made those two optional?</p>