The so-called "moving point problem" refers to the open problem that there are one or more moving points in the topic drawing, which move on a straight line, ray or arc. The key to solve this kind of problem is to seek quietness in movement and use relevant mathematical knowledge flexibly to solve the problem.

The "moving point problem" has many kinds of questions and innovative significance. It is a hot and difficult point to examine students' ability to analyze and solve problems, including spatial concept, application consciousness and reasoning ability.

The triangle, quadrilateral, function image and other graphics are studied from the perspective of transformation and motion change. The properties and changes of graphics are explored and discovered through the research methods of "symmetry and motion of moving points", and the concept of space and reasonable reasoning are infiltrated in the process of solving problems. Observe the changes of graphics in the process of moving points, understand the situation of graphics in different positions, and do a good job in the calculation and reasoning process. Finding the unchangeable property in the process of change is the basic idea to solve the problem of "moving point" in mathematics, and it is also the core mathematical essence in dynamic geometry mathematics.

Test center 1: Establish the resolution function (or function image) of the moving point problem.

Function reveals the changing law between quantity and quantity in the process of movement change, which is an important content of junior middle school mathematics. The fixed point problem embodies a functional idea. Because of the change of the conditional motion of a point or figure, there is a changing relationship between the unknown quantity and the known quantity, which is the functional relationship in the fixed point problem.

Test site 2: dynamic geometry problem

The problem of point motion, linear motion and shape motion is called dynamic geometry problem. It mainly takes geometry as the carrier, motion changes as the main line, integrates multiple knowledge points, and integrates various problem-solving ideas into one problem. This kind of problem is comprehensive and requires high ability, which can comprehensively examine students' practical operation ability, spatial imagination ability and problem-solving ability.

The characteristics of dynamic geometry-the background of the question is a special figure, and the examination of the question is also a special figure, so we should grasp the relationship between generality and particularity; In the process of analysis, we should pay special attention to the characteristics of graphics (special angle, the nature of special graphics, the special position of graphics. The problem of moving points has always been a hot topic in the senior high school entrance examination. In recent years, the particularity in sports has been investigated and explored: isosceles triangle, right triangle, similar triangles, parallelogram, trapezoid, special angle or its trigonometric function, maximum line segment or area.

Test site 3: double moving point problem

Dynamic problem is a hot topic in mathematics of senior high school entrance examination in recent years. This kind of question contains a lot of information, among which the double-action question, which is famous for its flexibility, has become a hot topic in the senior high school entrance examination. The double-action question requires students to have high information acquisition and processing ability. When solving problems, we need to observe and study the problems from the perspective of movement and change, and explore the whole process of movement and change, paying special attention to the invariants, unchanging relationships or special relationships between movement and change, and taking stillness in movement and seeking movement in stillness.