Construction 1.2 Constructing of a perpendicular bisector of a segment  $m( \overline{AB})$ and the midpoint of the segment
a.  Construct a circle with center at A whose radius is $m( \overline{AB})$.
b. Construct a circle with center at B  whose radius is $m( \overline{AB})$.
c. Find the points of intersection of these two circle.
d. Use these two points to to contruct the perpendicular bisector of  $ \overline{AB}$.
e. The intersection of the perpendicular bisector and  $ \overline{AB}$ is the midpoint. 
e. Use the Show/Hide Object Tool to hide the circles. 
Why is this a perpendicular bisector?

A = (0.6254891962193221, -1.4149672139694434)
B = (5.392070874861575, -1.3551356447814653)
a = Segment(A, B)