Mathematics
In each of the given figures; PA = PB and QA = QB.
(i)
(ii)
Prove in each case, that PQ (produce, if required) is perpendicular bisector of AB.
Hence, state the locus of the points equidistant from two given fixed points.
Locus
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Answer
(i) Join PQ which meets AB in D.
Given, PA = PB.
∴ P is equidistant from A and B. Thus, P lies on the perpendicular bisector of AB.
Given, QA = QB.
∴ Q is equidistant from A and B. Thus, Q lies on perpendicular bisector of AB.
Thus, both P and Q lie on the perpendicular bisector of AB.
Hence, proved that PQ is the perpendicular bisector of AB.
(ii) Join PQ which meets AB in D.
Given, PA = PB.
∴ P is equidistant from A and B. Thus, P lies on the perpendicular bisector of AB.
Given, QA = QB.
∴ Q is equidistant from A and B. Thus, Q lies on perpendicular bisector of AB.
Thus, both P and Q lie on the perpendicular bisector of AB.
Hence, proved that PQ is the perpendicular bisector of AB.
Hence, locus of the points which are equidistant from two fixed points, is the perpendicular bisector of the line joining the fixed points.
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