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<!doctype html>
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<title>Geometry - Reflection</title>
<script src="images/reflect.js" type="text/javascript"></script>
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<meta name="description" content="Learn about reflection in mathematics: every point is the same distance from a central line." />
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<h1 align="center">Reflection</h1>
<p class="center">Reflections are everywhere ... in mirrors, glass, and here in a lake. <i><br />
... what do you notice ?</i></p>
<div class="centerfull">
<div class="boxa"><img src="images/reflection-parinacota.jpg" width="299" height="205" alt="Reflection in Lake" /></div>
<div class="boxa"><img src="images/reflection-parinacota1.jpg" width="300" height="205" alt="Reflection Illustrated" /></div>
</div>
<p align="center">Every point is the <span class="large">same distance from the central line !</span>
</p>
<p align="center"><i>... and ...</i></p>
<p align="center">The reflection has <span class="large">the same size </span>as the original image</p>
<p align="center">The central line is called the <b>Mirror Line</b> ...</p>
<p align="center"><img src="images/reflection-ud.svg" alt="reflection up-down" /></p>
<p>&nbsp;</p>
<table border="0" align="center">
<tr>
<td><img src="images/flame-mirror.jpg" width="156" height="214" alt="flame mirror center line" /></td>
<td valign="top">&nbsp;</td>
<td align="center" valign="top">
<h2>Can A Mirror Line Be Vertical? </h2>
<p>Yes. <br />
Here my dog &quot;Flame&quot; shows a <br />
Vertical Mirror Line (with a bit of photo magic)</p></td>
</tr>
</table>
<table border="0" cellpadding="2" align="center">
<tr align="center">
<td colspan="3"><p> In fact Mirror Lines can be in <b>any direction</b>.<br />
Imagine turning the top image in different directions:</p></td>
</tr>
<tr align="center">
<td><img src="images/reflection-lr.svg" alt="Left-Right Reflection" /></td>
<td>&nbsp;</td>
<td><img src="images/reflection-75.svg" alt="75 Degrees Reflection" /></td>
</tr>
</table>
<p>&nbsp;</p>
<div class="center80">
<p align="center"><span class="larger">A reflection is a <b>flip</b> over a line</span><br />
</p>
</div>
<h3>You can try reflecting some shapes about
different mirror lines here:
</h3>
<script type="text/javascript">reflectMain();</script>
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<h2>How Do I Do It Myself?</h2>
<p>Just approach it step-by-step. For <b>each corner</b> of the shape:
</p>
<table border="0" cellpadding="2">
<tr>
<td colspan="3"></td>
</tr>
<tr valign="top">
<td width="33%"><span class="large">1.</span> Measure from the point to the mirror line (must hit the mirror line at a <a href="../rightangle.html">right angle</a>)</td>
<td width="33%"><span class="large">2.</span> Measure the same distance again on the other side and place a dot.</td>
<td width="33%"><span class="large">3</span>. Then connect the new dots up!</td>
</tr>
<tr align="center">
<td><img src="images/reflect-step1.jpg" width="85" height="109" alt="Step 1" /></td>
<td><img src="images/reflect-step2.jpg" width="140" height="109" alt="Step 2" /></td>
<td><img src="images/reflect-step3.jpg" width="135" height="99" alt="Final Reflect" /></td>
</tr>
</table>
<h2>Labels</h2>
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/reflect-labels.gif" width="228" height="84" alt="Mirror Image Prime" /></p>
<p>It is common to label each corner with letters, and to use a little dash (called a <b>Prime</b>) to mark each corner of the reflected image.</p>
<p>Here the original is <b>ABC</b> and the reflected image is <b>A'B'C'</b></p>
<h2>Some Tricks</h2>
<div class="center80">
<p style="float:left; margin: 0 10px 5px 0;"><img src="images/reflect-x.gif" width="150" height="161" alt="Reflect About X Axis" /></p>
<h3>X-Axis</h3>
When the mirror line is the x-axis <br />
we change each (x,y) into <b>(x,&minus;y)</b>
<p>&nbsp;</p>
</div>
<div class="center80">
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/reflect-y.gif" width="228" height="84" alt="Reflect About Y Axis" /></p>
<h3>Y-Axis</h3>
<p>When the mirror line is the y-axis<br />
we change each (x,y) into <b>(&minus;x,y)</b></p>
</div>
<div class="center80">
<h3>Fold the Paper</h3>
<p>And when all else fails, just fold the sheet of paper along the mirror line and then hold it up to the light !</p>
</div>
<p>&nbsp;</p>
<div class="questions">
<script type="text/javascript">getQ(6716, 6717, 3346, 3344, 3345, 3347, 5152, 5153, 841, 842);</script>&nbsp;
</div>
<div class="related">
<a href="symmetry-reflection.html">Reflection Symmetry</a>
<a href="transformations.html">Transformations</a>
<a href="rotation.html">Rotation</a>
<a href="translation.html">Translation</a>
<a href="index.html">Geometry Index</a>
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