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The question is: if $a$ and $b$ are any two numbers, what symmetry statement can be made about the points $(a, b)$ and $(b, a)$?

I'm not sure whether this is a symmetry statements and whether it is the correct solution, but here's what I get

"the points $(a, b)$ and $(b, a)$ are symmetric with respect to the quarters if $a$ and $b$ have different signs"

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    $\begingroup$ They are symmetric with respect to the main diagonal $\endgroup$ – Hagen von Eitzen Feb 10 '15 at 10:48
  • $\begingroup$ Ah, you were first :P $\endgroup$ – mathreadler Feb 10 '15 at 10:53
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They are equidistant to the line $x=y$, i.e. they "mirror" each other in this line.

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