Question
Let $G$ be the group of rotations of a plane about a point $P$ in the plane. Thinking of $G$ as a group of permutations of the plane, describe the orbit of a point $Q$ in the plane. (This is the motivation for the name "orbit.")
Step 1
First, consider the group of rotations $G$ about a point $P$. Each rotation in $G$ can be represented by an angle $\theta$ such that $0 \leq \theta < 360^\circ$ (or $0 \leq \theta < 2\pi$ in radians). Show more…
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