A rotation in the plane is determined if we fix its center and the angle of rotation (with respect to an established orientation). If P is a point in the plane and P' is its image, the vector P'O  is obtained by rotating the given angle corresponding  vector PO:

P'=P+Giro(PO)

The only fixed point of a rotation if the center.

Rotations preserve angles, distances and the orientation.

In the figure we see what is the image of a triangle by a rotation. You can check how the rotations behave in the plane, modifying the center and angle of rotation  and the vertices of the triangle.