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52 lines
2.4 KiB
HTML
52 lines
2.4 KiB
HTML
<div class="book-prose">
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<h2 id="history" class="book-prose__heading">History</h2>
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<p>
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Locus ideas emerged from classical compass-and-straightedge geometry and later became a core part
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of analytic geometry and optimization problems.
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</p>
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<h2 id="checkpoints" class="book-prose__heading">Checkpoints</h2>
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<details class="book-question">
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<summary class="book-question__prompt">Describe the locus of points 5 cm from point \(A\).</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> A circle center \(A\), radius 5 cm.</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">What is locus of points equidistant from \(A\) and \(B\)?</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> Perpendicular bisector of segment \(AB\).</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">Points within 2 m of line \(l\): describe region.</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> Strip between two parallels 2 m from \(l\), including boundaries if “within or equal to”.</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">Points equidistant from intersecting lines \(p,q\): what locus?</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> The two angle bisectors of lines \(p,q\).</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">Why can a locus answer be a region instead of a curve?</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> Inequality conditions describe many points satisfying a distance range.</p>
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</div>
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</details>
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<h2 id="applications" class="book-prose__heading">Applications</h2>
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<ul>
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<li><strong>Cell/Wi-Fi planning:</strong> coverage zones around transmitters.</li>
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<li><strong>Urban design:</strong> buffer distances from roads or facilities.</li>
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<li><strong>Robotics:</strong> safe navigation boundaries and target zones.</li>
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</ul>
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<h2 id="references" class="book-prose__heading">References</h2>
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<ul>
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<li>Standard high-school geometry content on loci and construction.</li>
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<li>Analytic geometry materials linking loci to equations.</li>
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</ul>
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</div>
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