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.

Choose basic geometric figures, let students experience the process of exploration, examine students' independent inquiry ability based on ability, and promote the cultivation of students' problem-solving ability.

To observe the changes of the graph in the process of moving points, it is necessary to know the situation of the graph in different positions in order to 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.

It is known that the numbers corresponding to two points A and B on the number axis are-1 and 3 respectively, and point P is the moving point on the number axis, and its corresponding number is x. 。

(1) If the distances from point P to point A and point B are equal, find the number corresponding to point P;

(2) Is there a point P on the number axis, so that the sum of the distances from point P to point A and point B is 6? If it exists, request the value of x; If it does not exist, explain the reasons;

(3) Point A and Point B move to the right at two unit lengths/min and 1 unit length/min respectively, while Point P moves from Point O to the left at six unit lengths/min. When encountering a, point P immediately moves to the right at the same speed, and keeps going back and forth between point A and point B to find the total distance that point P has traveled when point A and point B coincide.

Moving point A moves from the origin to the negative direction of the number axis, and moving point B also moves from the origin to the positive direction of the number axis. After 3 seconds, the two points are separated by 15 unit lengths.

It is known that the speed ratio of moving points A and B is 1: 4. (speed unit: unit length/second).

(1) Find the speed of two moving points, and mark the positions of point A and point B when they move from the origin for 3 seconds on the number axis; (2) If the two points A and B move from the position in (1) to the negative direction of the number axis at the same time, the origin will be right in the middle of the two moving points in a few seconds;

(3) In (2), when point A and point B continue to move in the negative direction of several axes at the same time, another moving point C starts from the position of point B and moves to point A at the same time. When it meets point A, it immediately returns to point B, then immediately returns to point A, and so on, until point B catches up with point A, and C immediately stops moving.

If point C has been moving at a constant speed of 20 unit lengths per second, how many unit lengths has point C moved from the start point to the end point?