Your friend constructs 𝑋𝑌 so that it is perpendicular to and contains the midpoint of 𝐴𝐵. He claims that 𝐴𝐵 is the perpendicular bisector of 𝑋𝑌. What is his error?

Answer 1

Heck, just draw the line AB. Then pick a point X close to the line and Y far away from the line.

While XY is the pb of AB, AB is not necessarily the pb of XY.