In recent years, dynamic questions have become the common content of the final questions in the senior high school entrance examination mathematics papers, with some types such as dynamic, linear and graphic. The presentation method is rich and colorful, which strengthens the integration and connection of various knowledge points, has a strong degree of discrimination, accounts for a high proportion, and has certain challenges.

To solve the moving point problem, we should "stop with static braking", that is, turn the dynamic problem into a static problem to solve it. The general method is to grasp the invariants of change. Firstly, according to the meaning of the topic, the change of variables in the topic is clarified and the related constants are found. Secondly, according to the geometric properties and mutual relations in the graph, a basic relationship is found, and the related quantities are expressed by the expression of an independent variable. Then according to the requirements of the topic, according to the knowledge of geometry and algebra to solve.

The basic feature of linear motion problem is that in the process of motion change, some straight lines or line segments keep the same positional relationship such as vertical and parallel, while the length of some line segments changes. This kind of problem usually uses the knowledge of right triangle, quadrilateral, congruence and similarity to establish the quantitative relationship between line segments, so as to solve the problem.

The problem of graphic movement is generally combined with graphic transformation. In the process of graphic movement, only the position changes, but the size and shape generally remain unchanged. Therefore, translation, rotation, symmetry, parallelism, congruence, isosceles triangle and other knowledge can often be used to solve such problems.

Formula of fixed point problem

1, the distance between two points on the axis. It can be expressed in absolute value, that is, the absolute value of the difference between two points. For example, if the numbers represented by points A and B on the number axis are A and B, then AB=|a-b| or | B-A |.

2. A moving point on the number axis is represented by a letter. It can be solved by addition or subtraction of rational numbers, that is, adding or subtracting the distance of the moving point from the number indicated by the starting point, adding in the positive direction and subtracting in the negative direction. For example, the number corresponding to point A on the number axis is-1, and point P starts from point A and moves to the right at a speed of 2 unit lengths per second. Let the movement time be t, then the number represented by point P is-1+2t.

3. The midpoint of the line segment between any two points on the number axis. The sum of the numbers represented by two points is divided by two. If the points on the number axis represent numbers A and B, then the number represented by the midpoint of the line segment AB is (a+b)/2.