(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose f is an isometry that fixes O (origin). Prove f preserves midpoints of line segments.

3. The attempt at a solution

Geometricallly, f could be a reflection in which case it would not preserve the mid point of any line segment that does not intersect the origin anywhere.

So I don't see a proof at all and infact sees a mistake.

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# F preserves midpoint?

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