= Point reflection
{title2=$x\mapsto2c-x$}
{wiki}
A <point reflection> about $c$ sends each point $x$ to $2c-x$. The point $c$ is the midpoint of $x$ and its image, and applying the map twice is the identity. It is a <Euclidean isometry> since $(2c-x)-(2c-y)=-(x-y)$ preserves the <Euclidean norm>. In the <Euclidean plane> it is a <rotation> through $\pi$; in <dimension> $n$ its <determinant> is $(-1)^n$, so it reverses <orientation> exactly in odd <dimension>. A figure invariant under this map has $c$ as a <center of symmetry>.
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