In this figure, a line through points x & y will be perpendicular to a b but not bisects it be unrelated to a b bisect a b but not perpendicular or be the perpendicular bisector of a b

From the figure, its clear that the compass drew arcs like below:

With A as centre, and more than half of the length of AB as radius, one arc is drawn.

With the same radius, with B as centre, another arc is drawn.

The points of intersections of the arcs are X and Y.

Clearly, this is the construction of a perpendicular bisector of the line segment AB.

Hence, if we draw a line segment through XY, it will be a perpendicular bisector of AB.