Would the image of a circle of radius r, center P under a reflection through its center remain in the same position? I am guessing that it is, but unfortunately I've found no other sources that verify this answer.
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Yes it is... you can proof this using coordinate geometry – QuIcKmAtHs Jan 23 '18 at 05:18
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Yes. it would be. Remember that any line through the circle's centre is the diameter and it splits the circle into two semicircles, say $A$ and $B$. Reflecting in the diameter reflects $A$ onto $B$ and $B$ onto $A$. Thereby the circle remains the same. – For the love of maths Jan 23 '18 at 05:26
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See https://math.stackexchange.com/questions/1693953/if-the-reflection-of-the-hyperbola-xy-4-in-the-line-x-y-1-0-is-xy – lab bhattacharjee Jan 23 '18 at 05:31
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The geometry stays the same,that is we still see the same graph.
The points on the circle move around such that their images under the reflection form the same circle.
Mohammad Riazi-Kermani
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