Define rotations, reflections, and translations using geometric language: angles, circles, perpendicular/parallel lines, and segments.
Identify a rotation from center-distance and angle facts
Problem
From these facts, identify the center and angle of rotation: \(P\) and \(P'\) are \(\text{both}\) \(5~\text{units}\) from \(O\) and angle \(POP'\) is \(90^{\circ}\) counterclockwise
Rotation facts fit together around one common reference point. Equal distances from that point identify the circle on which the original and image lie, while the directed central angle tells how one radius turns into the other; reading those two invariants together supplies the defining data.
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