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| Locus of points equidistant from two given points |
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| Mark two points M and N, 6 cm apart. |
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| Locate points P1 and P2 on either side of AB such that |
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| P1M=P1N=3.5 cm |
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| Locate points Q1 and Q2 such that Q1M = Q2M = 4.5 cm |
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Observe the pattern of geometric figure formed. The geometric figure formed seems to be a line. Join all these points. You get a line. Let
this intersect MN at O. Measure OM and On. Measure  . |
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| You will find that
= 90o . 1.e., QO
^MN. Take some other point K on this line l say k. Measure KM and KN. You will find that KM = KN. |
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| Observe that line l is perpendicular bisector of MN and all points on MN are equidistant from M and N. |
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| In other words: |
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| The locus of points equidistant from two given points (M and N) is the perpendicular bisector of the line joining those two given points (M, N)”. |
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| Thus, every point satisfying the given condition (s) is a point on the locus and conversely every point of the locus must satisfy the condition(s). |
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