Rotation is a geometric transformation that turns every point of an object around a specific center point by a certain angle. This transformation preserves the congruence (shape and size) of the object, but its orientation can change.
Key aspects of rotation:
Center of Rotation (C): The fixed point around which the rotation occurs.
Angle of Rotation (θ): The amount of turn. If the angle is positive, the rotation is counter-clockwise. If the angle is negative, the rotation is clockwise.
Given a center point C and a directed angle θ. Rotation with center C by an angle θ, denoted by ρC,θ or R(C,θ), is defined as a transformation that maps:
Point C to itself (C′=C).
Any point P to a point P′ such that CP=CP′ (the distance from the center to the point is equal to the distance from the center to the image) and the angle formed by ray CP and ray CP′ is θ.
