In a plane, a figure rotates a certain angle around a fixed point to get the change of another figure, which is called rotation. This fixed point is called the rotation center, and the rotation angle is called the rotation angle. If point A on the graph rotates to point A', then these two points are called corresponding rotation points.

nature

The rotation of a graph means that every point on the graph moves around a fixed point on the plane at a fixed angle, and the distance from the corresponding point to the rotation center is equal. The included angle between the corresponding point and the straight line connecting the rotation center is equal to the rotation angle.

The figure before and after rotation is congruent, that is, the size and shape of the figure before and after rotation have not changed. The center of rotation is the only fixed point. The included angle of a set of corresponding points is equal to the rotation angle.

Central symmetry

1, central symmetry: If one graph can overlap another graph after rotating 180 degrees around a certain point, then we say that these two graphs form central symmetry.

2. Centrally symmetric figure: If a figure can overlap itself after rotating 180 degrees around a certain point, then we say that this figure forms a centrally symmetric figure.

Nature:

On the congruence of two graphs with central symmetry. For two graphs with central symmetry, the straight lines connecting the symmetrical points pass through and are equally divided by the symmetrical center. For two figures with symmetrical centers, the corresponding line segments are parallel (or on the same straight line) and equal.

Symmetric transformation of points

1, the characteristics of points symmetrical about the origin. When two points are symmetrical about the origin, the signs of their coordinates are opposite, that is, the symmetrical point of point P(x, y) about the origin is P'(-x, -y).

2. About the characteristics of points that are axisymmetrical about X axis. When two points are symmetrical about X axis, in their coordinates, X is equal, and the sign of Y is opposite, that is, the symmetrical point of point P(x, y) about X axis is P'(x, -y).

3. On the characteristics of the point symmetrical about the Y axis. When two points are symmetrical about Y, Y is equal, and the sign of X is opposite in its coordinates, that is, the point where P(x, y) is symmetrical about Y is P'(-x, y).