The key: turn actions into static ones and discuss them in different categories. The key to solving the problem of moving point is to grasp the moving point. It is necessary to turn the moving point into a static one, and find the breakpoint (side length, moving point speed, angle and the equivalence relation of a given graph, etc.). ), establish the required equivalent algebra, break through the problem, find out the unknown and so on. The fixed point problem is the main idea. For example, when moving at a certain speed, the position of the point can be indicated after setting the time; Another example is the moving point of a function. Try to set a variable, where y is represented by x as much as possible. You can use this point as the moving point to calculate.

Steps: ① draw a graph; ② Table segment; ③ Column equation; ④ Find the positive solution.

Moving point problem on number axis

The problem of moving point on the number axis is inseparable from the distance between two points on the number axis. In order to facilitate the analysis of such problems, we must first clarify the following issues:

1. The distance between two points on the number axis is the absolute value of the coordinate difference corresponding to these two points, that is, the difference between the number on the right and the number on the left is subtracted. That is, the distance between two points on the number axis = the number represented by the right point-the number represented by the left point. The following is an example of absolute value removal:

Known: a

2. When a point moves on the number axis, because the right direction of the number axis is positive, the speed of moving to the right is regarded as positive speed, and the speed of moving to the right is regarded as negative speed. In this way, the coordinates of the point after moving can be directly obtained by adding the moving distance of the point on the basis of the starting point. That is, the number represented by point A is A, and the number represented by the left shift of unit B is A-B; After moving unit b to the right, the number is a+B.

3. The number axis is the product of the combination of numbers and shapes, and the motion analysis of points on the number axis should be combined with graphics. The path formed by the movement of points on the number axis can be regarded as the sum and difference relationship of line segments on the number axis.

Brief introduction to the problem: As shown in the figure below, there is a number axis with the origin of O, and the number corresponding to point A is-1 12. Point A translates along the number axis at a constant speed and reaches point B through the origin.

(1) If OA=OB, what is the number corresponding to point B?

(2) The time from point A to point B is 3 seconds. Find the moving speed of this point.

(3) Passing through point K at a uniform speed from point A to point C along the number axis, taking 9 seconds, KC=KA, and finding the numbers corresponding to point K and point C respectively.

Number of test sites; Compare the lengths of line segments. Topic: the combination of numbers and shapes (the topic of the combination of numbers and shapes will be introduced later).

Analysis (1) shows that the number corresponding to point B is the reciprocal of the number corresponding to point A, because OA = OB.

(2) Find the distance of AB first, and then solve it according to speed = distance/time;

(3) Find the distance of AC to get the number corresponding to point C, and then get the number corresponding to point K by KC=KA.

Solution: (1)∫OA = ob, the number corresponding to point A is112, and the number corresponding to point B is ∴112;

(2) [112-(-12)] 3 = 3 3 =1.So the moving speed of this point is1per second.

(3) 1× 9 = 9, 9 ÷ 2 = 4.5, and the number corresponding to ∴ point c is ∴112+9 = 712.

The number corresponding to point K is-1 12+4.5 = 3. So the number corresponding to point C is 7 12, and the number corresponding to point K is 3.

Comments examined the number axis and distance, mastered the solution of the distance between two points on the number axis.