Dear Melanie:

On a real axis, a number and its negative are symmetric with respect to the origin. Put another way, the two points, say, 2 and (-2) are reflections of each other in the vertical axis. Does it sound plausible that reflection of a reflection shows the thing itself?

Try playing with two mirrors. When you look into a mirror your right side appears on the left and the left side on the right. Arrange two mirrows so that you can see in one what is reflected in the other. Sides will appear the right way out.

Returning to numbers, regardless whether a given number is negative or positive, reflecting it once in the origin will produce a number on the opposite side of the origin. Doing it twice will leave the number where it started.

Regards

Copyright © 1996-2009 Alexander Bogomolny

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