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Question

In given figure AB is a line segment and line l is its perpendicular bisector. If a point P lies on l, show that P is equidistant from A and B
569983_80fb5f400f39438b9eb4703ef556abc2.png

Solution
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Given AB is a line segment and l is perpendicular bisector. if point p lies on l.

Join P to A and B
The perpendicular l passe through line AB, cut on C

Then C is the midpoint of AB

Then AC=BC

In ΔPCA And ΔPCB

AC=BC (Given M is the Midpoint of AB)

PCA=PCB=900 (l is the perpendicular on AB)

PC=PC

ΔPCAΔPCB

PA=PB [henceproved]

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