Good question! It is always possible to try to graph and get a rough idea, but there is an important property that can also help:

• If a line $\ell$ is the perpendicular bisector of $\overline{AB}$, then any point $C$ on the perpendicular bisector must be the same distance from $A$ as it is to $B$. If the distances are not equal, then $C$ is not on the perpendicular bisector.

This property is a nice way to check for this problem. Hope this helps!