Perpendicular bisector/Distance condition/Fact/Proof/Exercise

Let ${\displaystyle {}A,B}$ be different points in a Euclidean plane. Show that the perpendicular bisector of ${\displaystyle {}A}$ and ${\displaystyle {}B}$ consists of all those points that have the same distance to ${\displaystyle {}A}$ and to ${\displaystyle {}B}$.