Let’s take lines AB & XY
Now,
XY ⊥ AB
If XY bisects AB as well
i.e. if O is the midpoint of AB
i.e. if OA = OB
Then, XY is perpendicular bisector of AB.
Perpendicular bisector means
 Line is perpendicular

Line bisects the other line
Here,
 XY ⊥ AB

And OA = OB
∴ XY is perpendicular bisector of AB.