Prove using coordinate geometry: if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Let be A(2,2) and B(4, 4) two points, let be C the point which is on the perpendicular bisector of the segment AB, so the coordinate of C must be 
C(2+4 / 2,  2 + 4 /2) = C(3,3)
C is equidistant from the endpoints of the segment.
proof
vect AC= (1, 1), and vect CB= (1, 1), the length of each vect is 
CB= sqrt2, and AC=sqrt2, so it is prooved that AC=CB, C is equidistant to the two endpoints 

Agc and bgd are vertical angles