Why do two symmetrical points form a perpendicular line to their reflection axis?

Question

Question is the title. I know that this is the case, but I don't know why. You can take two points that are at the same distance from an axis but whose line doesn't form a 90° angle to the axis and they wouldn't be symmetrical, so why is this?

Answer 1

Let $A,B$ be symmetric with respect to line $\ell$. Then each point on $\ell$ is at equal distance to $A$ and $B$, so $\ell$ is bisector of segment $AB$ and this is well known perpendicular to $AB$.