If r and s are two points in the plane, the perpendicular bisector of is the set of all points equidistant from r and s.
a. true
b. false

The Meaning of term ,  perpendicular bisector, is that it divides the line segment into two congruent parts.

and Secondly if you will take any point on the perpendicular bisector ,it will be equidistant from both the points for which you have drawn perpendicular bisector.

So, if R and S are two points in the plane, the perpendicular bisector of is the set of all points equidistant from R and S.

So, the given statement is True Statement.

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.