Locus of points equidistant from two given points

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Mark two points M and N, 6 cm apart.

Locate points P₁ and P₂ on either side of AB such that

P₁M=P₁N=3.5 cm

Locate points Q₁ and Q₂ such that Q₁M = Q₂M = 4.5 cm

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 .

You will find that = 90^o . 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.

Observe that line l is perpendicular bisector of MN and all points on MN are equidistant from M and N.

In other words:

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)”.

Note:

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).