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153 lines
6.3 KiB
HTML
153 lines
6.3 KiB
HTML
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<title>Midpoint of a Line Segment</title>
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<h1 align="center">Midpoint of a Line Segment</h1>
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<div class="def">
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<h3>Coordinate Point</h3>
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<p style="float:right; margin: 0 0 5px 20px;"><img src="../images/coordinates-cartesian-sm.gif" alt="graph with point (12,5)" width="164" height="120" /><br>
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Here the point <b>(12,5)</b> is<br />
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12 units along, and 5 units up</p>
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<p>We can use <a href="../data/cartesian-coordinates.html">Cartesian Coordinates</a> to locate a <a href="../geometry/point.html">point</a> by <b>how far along</b> and <b>how far up</b> it is:</p><div style="clear:both"></div>
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</div>
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<p>And when we know <b>both end points</b> of a <a href="../geometry/line.html">line segment</a> we can find the <b>midpoint "M"</b> (try dragging the blue circles):</p>
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<script src="../geometry/images/geom-line-equn.js"></script>
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<script>geomlineequnMain('mid');</script>
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<h2>Midpoint of a Line Segment</h2>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/midpoint-line-a.svg" alt="midpoint line between A and B" /></p>
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<p>The midpoint is <b>halfway</b> between the two end points:</p>
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<ul>
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<li>Its<b> x value </b> is halfway between the two x values</li>
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<li>Its <b> y value</b> is halfway between the two y values</li>
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</ul>
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<p>To calculate it: </p>
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<ul>
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<li>Add both "x" coordinates, divide by 2</li>
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<li>Add both "y" coordinates, divide by 2</li>
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</ul>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/midpoint-line.svg" alt="Midpoint of Line" /></p>
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<div style="clear:both"></div>
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<p>As a formula:</p>
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<p class="center large">M = (
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<span class="intbl">
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<em>x<sub>A</sub>+x<sub>B</sub></em>
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<strong>2</strong>
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</span> <span class="larger">,
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</span>
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<span class="intbl">
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<em>y<sub>A</sub>+y<sub>B</sub></em>
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<strong>2</strong>
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</span>
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<span class="larger">
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)</span></p>
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<div style="clear:both"></div>
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<div class="example">
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<h3>Example: What is the midpoint here?</h3>
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<p style="float:left; margin: 0 20px 5px 0;"><img src="images/midpoint-line-ex.gif" alt="Midpoint of Line" width="262" height="207" /></p>
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<p>Use the formula:</p>
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<p class="larger">M = ( <span class="intbl">
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<em>x<sub>A</sub>+x<sub>B</sub></em>
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<strong>2</strong>
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</span> <span class="larger">, </span> <span class="intbl">
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<em>y<sub>A</sub>+y<sub>B</sub></em>
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<strong>2</strong>
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</span> <span class="larger"> )</span></p>
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<p class="larger">M = ( <span class="intbl">
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<em>(−3)+8</em>
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<strong>2</strong>
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</span> <span class="larger">, </span> <span class="intbl">
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<em>5+(−1)</em>
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<strong>2</strong>
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</span> <span class="larger"> )</span></p>
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<p class="larger">M = ( 5/2, 4/2 )</p>
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<p class="larger">M = ( 2.5, 2 )</p>
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</div>
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<p> </p>
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<script type="text/javascript">getQ(527, 528, 1167, 7389, 7390, 7391, 7392, 7393, 7394, 1168);</script>
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</div>
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<div class="related">
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<a href="../equation_of_line.html">Equation of a Straight Line</a>
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<a href="../straight-line-graph-calculate.html">Straight Line Graph Calculator</a>
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<a href="../geometry/parallelogram-in-quadrilateral.html">Parallelogram In Any Quadrilateral</a>
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<a href="index.html">Algebra Index</a></div>
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Copyright © 2017 MathsIsFun.com
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