# Plane Reflection is Space Rotation

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## Theorem

Let $M$ be a straight line in the plane passing through the origin.

Let $s_M$ be the **reflection** of $\R^2$ in $M$.

Then $s_M$ is the rotation of the plane in space through one half turn about $M$ as an axis.

## Proof

This theorem requires a proof.Needs equations of space rotationYou can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{ProofWanted}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## Sources

- 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 28$. Linear Transformations: Example $28.4$