The so-called "moving point problem" refers to an open problem in which there are one or more moving points in a graph moving 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 key: seek quietness while moving.

Mathematical thought: classification thought function thought equation thought combination of number and shape thought transformation thought

Title 1: Establish the resolution function of the fixed point problem 1. Applying Pythagorean Theorem to Establish Resolution Function 2. The resolution function 3 is established by using the proportional formula. The function relation is established by drawing area method.

Thirdly, the function relationship is established by finding the graphic area. I) point motion problem. II) Linear motion problem. III) Surface motion problems.

Topic 3: similar triangles problem caused by moving points in functions

Generally, there are three solutions to the similar triangles problem caused by fixed points in functions. ① When finding the third vertex of similar triangles, we should first analyze the characteristics of the sides and angles of the known triangle, and then get whether the known triangle is a special triangle. According to the known edges in the unknown triangle and the possible corresponding edges of the known triangle, the discussion is classified.

(2) Or using the corresponding angles in the known triangle, using the knowledge of Pythagorean theorem, trigonometric function, symmetry, rotation and so on, the size of the middle side of the unknown triangle can be deduced.

(3) If the sides of two triangles are not given, first set the coordinates of the points to be solved, then use the resolution function to represent the length of each side, and then use the similarity to solve the equations.

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