Why do mirrors flip sideways (but not up side down)?

Have you ever wondered why mirrors appear to flip images sideways but not up side down?

That was the question raised by Physics Girl on Youtube – a simple question yet one of the mysteries of science only few can really explain. Mirror as we know it is an amazing amazing thing on earth that tell us literally (and psychologically) a great deal about how we see ourselves. But what do reflections tell us about the mirrors themselves? What exactly is a mirror… and how does it work?

Physics Girl vlogger Dianna Cowern demonstrated how the mirror works, “If I raise my right hand, the mirrored me raises her left hand, but if I put my hand up in the air, she also puts her hand up, not down. So what’s going on? The mirror is flipping the image, but it’s flipping it in the z-direction, that’s what’s causing all this confusion. If I could take my body and flip it through itself in the z-direction, I would get my mirror image.”