AB is a line-segment. P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B. Show that the line PQ is the perpendicular bisector of AB

A B is a line segment. P\ a n d\ Q are points on opposite sides of A B such that each of them is equidistant from the points A\ a n d\ B (in figure). Show that the line P Q is perpendicular bisector of A B .

Prove that the locus of a point equidistant from the extermities of a line segment is the perpendicular bisector if it.

A B 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 Bdot

A B 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 Bdot

Show that the line segments joining the mid-points of opposite sides of a quadrilateral bisects each other.

Two circles with centres A and B intersect each other at points P and Q. Prove that the centre-line AB bisects the common chord PQ perpendicularly.

Construct the perpendicular bisector of the line segment PQ.

Statement - 1 : If the perpendicular bisector of the line segment joining points A (a,3) and B( 1,4) has y-intercept -4 , then a = pm 4 . Statement- 2 : Locus of a point equidistant from two given points is the perpendicular bisector of the line joining the given points .

The given figure shows a circle with centre O. P is mid-point of chord AB. Show that OP is perpendicular to AB.

If a number of circles pass through the end points P and Q of a line segment PQ, then Prove that their centres lie on the perpendicular bisector of PQ.