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Why does a mirror reverse left and right but not up and down?

Stand in front of a mirror and raise your right hand. Your reflection raises what looks like its left hand. Yet the reflection's head is at the top and its feet at the bottom, not swapped.

Why does a mirror reverse left and right but not up and down? What does the mirror actually reverse, and why do we describe it the way we do?

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Point at the mirror. Which way does your reflection point?

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