Graph rotation properties:

After rotation, every point on the graph rotates around the rotation center at the same angle and in the same direction. The angle formed by the connecting line of any pair of corresponding points and the rotation center is the rotation angle, and the distances from the corresponding points to the rotation center are equal.

In a graph and its rotation graph, the distance between the corresponding points and the rotation center is equal, and the angle formed by the connecting line between any group of corresponding points and the rotation center is equal to the rotation angle; The corresponding line segments are equal and the corresponding angles are equal.

Extended data graph rotation method:

Take the five-pointed star as an example. The black five-pointed star is the original picture. When it rotates 72, it coincides with the original picture, which is called rotational symmetry. When a picture is rotated by 90 or180, it coincides with the original picture and is a rotationally symmetric figure. Then the degree of rotation is the rotation angle (let the angle be α 0

The symmetry of (1) point 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) The characteristics of the points that are symmetrical about the X axis.

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

(3) 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).

(4) Symmetry of the straight line y = x.

When two points are symmetrical about the straight line y=x, the abscissa and ordinate are reversed, that is, the symmetrical point of P(x, y) about the straight line y=x is P'(y, x).

(5) When two points are symmetrical about the straight line y=-x, the abscissa and ordinate are opposite to those before, that is, the symmetrical point of P(x, y) about the straight line y=x is P'(-y, -x).

Note: A straight line with y=x is the bisector of an angle passing through one or three quadrants, and a straight line with y=-x is the bisector of an angle passing through two or four quadrants.