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Chapter - 17

Loci

Locus : - Locus is a path traces out by a moving point satisfying certain given geometrical conditions.

Theorem – I

The locus of a point equidistant from the two fixed points is the perpendicular bisector of the line joining the fixed point.

Part – I

Every point which is equidistant from two fixed points A and B lies on the perpendicular bisector of AB.

Given : - A and B are two fixed point and a point P such that PA = PB.

To Prove : - P Lies on the perpendicular bisector of AB.

Construction : - A and B is joined. AB is bisected at M. PA, PB and PM are joined.

Proof : -

1. PA = PB AM = BM PM = PM	1. Given By construction Common
2.	2. S.S.S
3.	3. Statement (2)
4.	4. AMB is a straight line
5. = 900	5. Statements (3), (4)
6. i.e. Plies on the perpendicular bisector of AB.	6. Statement (5)

Part – II Conversely, every point on the perpendicular bisector of AB is equidistant from A and B.

Given: - Two given points A and B. P is any point on the perpendicular bisector ‘l’ of AB.

To Prove: - PA = PB

Proof: -

Hence every point equidistant from A and B lies on the perpendicular bisector of AB and every point on the perpendicular bisector of AB is equidistance from A and B.