Argghh, I'm not sure I can do this without smoke and mirrors or at the very least drawings.

A reflection is a transformation in the same plane as the mirror. A vertical transposition is impossible as the mirror conceptually does not exist in the required plane (it has zero thickness) In the limit if you consider the mirror as two dimensional, then the object and its relection are also two dimensional and the concept of a vertical transposition is meaningless.... on the other hand it could be because thats the way the fairies that live in the mirror like to paint you!

Pete M