Question

In each of the given figures; PA = PB and QA = QB.

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.

Answer 1

Construction: Join PQ which meets AB in D.

Proof: P is equidistant from A and B.

∴ P lies on the perpendicular bisector of AB.

Similarly, Q is equidistant from A and B.

∴ Q lies on perpendicular bisector of AB.

∴ P and Q both lie on the perpendicular bisector of AB.

∴ PQ is perpendicular bisector of AB.

Hence, locus of the points which are equidistant from two fixed points, is a perpendicular bisector of the line joining the fixed points.