Translation does not change the shape and size of the graph. After translation, the corresponding line segments are equal, the corresponding angles are equal, and the line segments connected by the corresponding points are equal. It is equidistant isomorphism and an affine transformation in affine space. It can be considered as the result of adding the same vector to each point or moving the center of the coordinate system. That is, if a known vector is a point in space, translate.
Conceptual description of mathematical translation;
Modern mathematics: the definition of translation has different forms in different books, including the following.
① On Euclidean plane (Euclidean space), move every point P to P' in the direction of known vector AA' so that PP'= AA'. The transformation generated in this way is called translation transformation along the vector AA' on the plane (space), which is referred to as translation or direct motion for short.
(2) In a plane, a graphic moves a certain distance along a certain direction, and such graphic movement is called translation.
③ Patterns or figures can slide in any direction. If its size and direction have not changed, then this movement is called translation.
Mathematics in primary schools: There is no clear definition of translation in primary schools, but we intuitively understand the phenomenon of translation through concrete examples, and get the movement experience by making known figures on grid paper after translation transformation. We think that translation is the movement of objects in a straight line, and there is no change in direction itself.
The above contents refer to Baidu Encyclopedia-Translation.