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55 lines
2 KiB
HTML
55 lines
2 KiB
HTML
<div class="book-prose">
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<p>
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A <strong>locus</strong> is the set of all points that satisfy a given condition. Loci connect
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geometric constructions with equations and constraints.
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</p>
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<h2 id="basic-loci" class="book-prose__heading">Basic loci patterns</h2>
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<ul>
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<li>Fixed distance \(r\) from point \(A\): a circle center \(A\), radius \(r\).</li>
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<li>Fixed distance from line \(l\): two parallel lines on each side of \(l\).</li>
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<li>Equidistant from points \(A,B\): perpendicular bisector of \(AB\).</li>
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<li>Equidistant from two intersecting lines: angle bisectors.</li>
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</ul>
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<h2 id="constructing-loci" class="book-prose__heading">Constructing loci</h2>
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<ol>
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<li>Translate condition into known locus type.</li>
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<li>Construct each required locus accurately.</li>
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<li>Find intersection of loci for final solution points/region.</li>
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</ol>
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<h2 id="inequality-regions" class="book-prose__heading">Loci and inequalities</h2>
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<p>
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Conditions like “distance at most 3 cm from line” describe a region, not a single line.
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</p>
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<p>
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Boundary inclusion matters:
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</p>
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<ul>
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<li>\(\le\): boundary included (solid)</li>
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<li>\(<\): boundary excluded</li>
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</ul>
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<h2 id="equation-links" class="book-prose__heading">Algebra links</h2>
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<p>
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Coordinate forms:
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</p>
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<ul>
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<li>Circle: \((x-h)^2+(y-k)^2=r^2\)</li>
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<li>Perpendicular bisector from equal-distance condition \(PA=PB\)</li>
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</ul>
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<h2 id="real-world-models" class="book-prose__heading">Modeling with loci</h2>
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<p>
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Loci are used for coverage regions, safe-distance boundaries, and optimal placement constraints.
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</p>
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<h2 id="exam-strategy" class="book-prose__heading">Exam strategy</h2>
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<ul>
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<li>Underline keywords: equidistant, fixed distance, within, at least.</li>
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<li>Draw boundaries first, then shade valid region.</li>
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<li>State whether endpoints/boundaries are included.</li>
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<li>Use intersections of loci to justify final points.</li>
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</ul>
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</div>
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