A reflection is like a mirror because a mirror shows the same figure put in a different position. You could reflect an image over the x-axis or y-axis without knowing the exact rules by knowing that when you reflect the image over the x-axis, you change the y coordinates, and when you reflect the image over the y-axis, you change the the x coordinates. Therefore, it's the opposite. The original figure and it's reflection is exactly equal distance from the line of symmetry because nor the size or shape changes, only the position, and the two figures match.
I think that we could determine the line of symmetry if we were given the points of the original figure and the image. When looking at two figures, we know which one is the transformation because one figure is the original, and the other is prime. So the figure that is plotted prime is the transformation figure.
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