If a and b are two points in the plane the perpendicular bisector of Ab is the set of all points equidistant from a and b?

The perpendicular bisector of the line segment connecting points ( A ) and ( B ) in the plane is a line that divides the segment into two equal parts at a right angle. Every point on this line is equidistant from points ( A ) and ( B ). This means that if you take any point ( P ) on the perpendicular bisector, the distance from ( P ) to ( A ) will be the same as the distance from ( P ) to ( B ). Thus, the perpendicular bisector is the locus of points satisfying this equidistance condition.