Nothing is flipped on the xy plane. The flipping happens on the Z-axis. Your reflection is a translation of yourself across the Z-axis into the mirror then a f

Nothing is flipped on the xy plane. The flipping happens on the Z-axis. Your reflection is a translation of yourself across the Z-axis into the mirror then a flip along the depth axis so that your reflection faces you. When you look at your face, both your left eye and your reflected left eye are still to your left relative to you. Same with your right eye. Your chin is the same. Your chin is below your actual nose and your reflected chin is still below your actual nose. All positions are PRESERVED along the xy plane. What flipped is the Z axis. Imagine you wearing face as a mask then flipping it inside out along the z-axis so that the face mask is now looking at you. That is the flipping that is going on... all other positional coordinates are preserved. People who say there is no "flipping" going on are completely wrong. There is a flip: on the z-axis.