`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`.

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 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

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. A X\ a n d\ B Y are two equal line segments drawn on opposite sides of line A B such that A X||B Y . If A B\ a n d\ X Y intersect each other at P , prove that (i) A P X~=B P Y (ii) A B\ a n d\ X Y bisect each other.

Find the equation of the right bisector of the line segment joining eth points A(1,0)a n d\ B(2,3)

A B is a line segment, A X and B Y are two equal line segments drawn on opposite sides of line A B such that AX||BY . If A B and X Y intersect each other at P , prove that triangle A P X~= triangle B P Y . A B and X Y bisect each other.

A B C\ a n d\ D B C are two isosceles triangles on the same bas B C and vertices A\ a n d\ D are on the same side of B C . If A D is extended to intersect B C at P , show that A P bisects " "/_A as well as /_D and A P is the perpendicular bisector of B C

Two chords A B\ a n d\ C D of a circle are parallel and a line L is the perpendicular bisector of A B . Show that L bisects C D

Find the equation of the right bisector of the line segment joining the points (a , b)a n d\ (a_1, b_1)dot