2. Rotation is the movement when the distance between each point and the same point is constant, which is called rotation around this point, and this point is called the rotation center of the object. So, it doesn't have to be around an axis.
3. Translation and rotation are relative, so when an object moves, the distance between any two points remains the same and will not be its mirror image. The motion of a point can always be regarded as translation.
Extension: 1. The shape and size of the image have not changed before and after translation, but the position has changed.
2. After the image is translated, the line segments connected by the corresponding points are parallel and equal.
3. The figures before and after rotation are congruent, that is, the size and shape of the figures before and after rotation have not changed.
4. The rotation center is the only fixed point.