Rotazioni

A rotation makes the plane “turn” about a fixed point by a given angle. We consider the case in which the centre is the origin.

Definition — Rotation about the origin

Given a rotation about the origin by an angle $\theta$, the formulae are: $(x;y)\mapsto(x';y') = (x\cos\theta - y\sin\theta;\ x\sin\theta + y\cos\theta).$ For $\theta = 90°$ (anticlockwise): $(x;y)\mapsto(-y;x)$. For $\theta = 180°$: $(x;y)\mapsto(-x;-y)$, which is the central symmetry with respect to the origin.

Links

Topics: Plane transformations
Concepts: Rotation · Central symmetry
Methods: Isometric transformations
Skills: Analytic geometry