What Is a Reflex Point?

If the one-to-one transformation of the plane to itself causes any connected line segment to pass through a fixed point and be squared by that point, then this one-to-one transformation is called point reflection transformation, referred to as point reflection, and the fixed point is called the reflection center or the center of symmetry The corresponding points are called point symmetrical points about the reflection center (center of symmetry), and the two corresponding figures under point reflection are called symmetrical points about the reflection center (center of symmetry).

Point reflection transformation is also called point-symmetric transformation or center-symmetric transformation. A kind

Point reflection has the following main properties:

1. One-to-one transformation f is a necessary and sufficient condition for point reflections: the corresponding line segments under f are parallel, opposite and equal;

2. The product of two point reflections with different centers is a translational transformation. As shown in the figure, the points of symmetry of points A and B with respect to O ₁ are A , B , and the points of symmetry with points A and B are O and A , respectively. B '' is parallel, in the same direction and equal, so the product of the reflections at these two points is a translational transformation;

3. The inverse transformation of point reflection is still point reflection;

4. The reflection center is the only two points. Any straight line passing through the reflection center point is a double line;

5. The product of translational transformation and point reflection is about point reflection centered on another point;

6. Rotating any one of the centrally symmetric figures 180 degrees around the center of symmetry must coincide with its corresponding figure. Therefore, a rotation with a rotation angle equal to ± 180 degrees is a point reflection about the center of rotation.

figure 1.