The mirror DOES flip one coordinate, the "hither" versus "yon" coordinate. If you hold a paper of text up against the mirror, and it looks mirrored, then you can notice that the original text ALSO looks inverted to you, if the paper is translucent. Right is right. Up is up. However, "hither" becomes "yon." Exactly like we would expect by looking at the math for reflection in a plane.