How to do the Moving Point Question 5, how to do the Moving Point Question

First of all, you have to figure out what the title means and how to move the point. Secondly, using some of the properties learned, the moving point problem is generally in geometric figures.

Upper and Sum Function Image.

This requires you to have a good grasp of the fundamental theorems and certain properties.

The above are the basic requirements. In addition to that, you need to be clear about the following:

1.According to the relationship of the topic, this moving point must be directly related to some quantities in the topic, which is the breakthrough.

2.Then, put the points on the concrete graph for analysis. Remember to think about it comprehensively, apply everything you've learned, and then filter for what is useful.

3.Finally, based on your analysis, look for the relationship, list some equities or inequalities, and find the solution.

Also, the moving point is generally very complex, and there will be many situations, so you need to have a wide range of ideas to do such a question. Otherwise, it's easy to make mistakes.

The time for the math exam may be relatively short, and it takes a lot of strength to complete it, not to mention that the last question is so difficult, which requires you to practice more.

Let me tell you a secret, mathematics is about practice makes perfect, if you usually do a large number of questions, just a test paper can be completed quickly, and the correct rate can be guaranteed.

Here's how to do the moving point problem:

The key to solving this kind of problem is to be still in motion and flexibly apply relevant mathematical knowledge to solve problems.

Method. Triangles, quadrilaterals, function images and other graphics are studied from the perspective of transformation and motion changes, and the properties and changes of graphics are explored and discovered through research methods and methods such as "symmetry and motion of moving points", and spatial concepts and reasonable reasoning are infiltrated in the process of problem solving.

Select basic geometric figures, let students go through the process of exploration, test students' autonomy with ability, and promote the cultivation of students' problem-solving ability.

The graph observes the changes of the graph during the movement of the moving point, and it is necessary to understand the situation of the graph in different positions in order to do a good job in the process of calculation and reasoning.

Finding the invariant property in change is the basic idea of solving the mathematical "moving point" problem, which is also the core mathematical essence of dynamic geometric mathematical problems.

It is known that the number corresponding to two points A and B on the number axis is , and the point p is the moving point on the number line, and the corresponding number is x

1) If the distance from point p to point a and point b is equal, find the number corresponding to point p;

2) Is there a point p on the number line, so that the sum of the distances from the point p to the point a and the point b is 6? If there is a costume, the value of x is requested; if not, the reason;

3) Point A and point B move to the right at the speed of 2 unit length minutes and 1 unit length minute respectively, and at the same time point P moves from point O to the left at the speed of 6 unit length minutes 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, find out when point A and point B coincide, what is the total distance of point P through the repentance stove?

Point A moves from the origin to the negative direction of the number axis, and at the same time, point B also moves from the origin to the positive direction of the number axis, and after 3 seconds, the two points are 15 units apart by 15 unit lengths

It is known that the velocity ratio of points A and B is 1:4 (unit of velocity: unit length in seconds).

1) Find the velocity of the two moving points, and mark the position of the two points A and B when they move from the origin for 3 seconds on the number axis; (2) If 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 is exactly in the middle of the two moving points after a few seconds;

3) In (2), when the two points A and B continue to move in the negative direction of the number axis at the same time, the other moving point C starts from the position of point B and moves to A at the same time, when it encounters A, it immediately returns to point B and moves towards point A, and so on until B catches up with A, C immediately stops moving

If point c is moving at a constant speed of 20 units of length and seconds, then what is the length of the distance traveled by point c from the beginning to the end of motion

The formula for solving the problem of the first moving point is as follows:

The problem of moving points on the number axis is inseparable from the distance between two points on the number line. In order to facilitate the analysis of such questions by first-year students, it is advisable to clarify the following questions first:

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 subtracted. That is, the distance between two points on the number line, the number represented by the right point, and the number represented by the left point.

When two points are moving on the number axis, the speed of the right movement is considered as a positive velocity, and the speed of the movement is considered to be a negative velocity, since the direction of the number axis to the right is a positive direction. In this way, adding the motion distance of the point on the basis of the starting point can directly obtain the coordinates of the point after the movement. That is, the number represented by a point is a, and the number represented by moving b units to the left is a b; The number represented by moving b units to the right is a+b.

3 The number axis is the product of the combination of numbers and shapes, and the analysis of the movement of points on the number axis should be analyzed in combination with the graph, and the path formed by the movement of the point on the number axis can be regarded as the sum and difference relationship of the upper part of the number axis. Source.

Example 1 It is known that there are three points a, b, and c on the number axis, representing the trace cleft group 24, 10, and 10, respectively, and two electronic ants and B are traveling in the same direction from the two points A and C, respectively, with a velocity of 4 units of seconds.

Q: How many seconds later, the sum of distances to a, b, and c is 40 units?

If B's velocity is 6 units of a second, and two electronic ants and B are moving in opposite directions at the same time from points A and C, where on the number line do B meet?

Under the condition of , when the sum of the distances to a, b, and c is 40 units, the U-turn returns. Q: Can B still meet on the number line? If so, find the point of encounter; If not, please explain why.

1. The moving point P starts from the point D, and moves along the line section DA, AB to the point B, and the speed is 2cm s; then when Ts is moved, PD=2T

ap=ad-pd=9-2t

The moving point q starts from the point A and moves along the line from the AB to the point B, the speed is 1cm s, and when the motion TS, AQ=T

Pa=aq i.e. 9-2t=t then t=3s

So when t=3s, pa=aq

2. Let p catch up with Q after TS, the distance of Q is Qa=T, and the distance of P is 2T, and the P point and Q point coincide, Pa=Qa

The distance of motion at point P can be expressed as, AD+PA=AD+QA=2T, that is, 9+T=2T is solved to obtain T=9S

So when t=9s, p can catch up with point q

1) When P is on DA, PA=AD-2T=9-2T (0=When P is on AB, PA=2( (AQ=T (0=PA=AQ9-2T=T

When t=3s point p moves on the DA, at t=3s, it can make pa aq2)2(

When t=9st=9s, point p can catch up with point q.

The dynamic complex point problem in junior high school mathematics can be roughly divided into two kinds of dynamics.

Bai point 1. The point of movement.

du: This kind of moving point gives the direction of movement dao and the speed of movement, and we mainly represent the length of some line segments according to the speed of movement time = distance. According to the position of the moving point, the line segment can be divided into those that have been traveled (represented by speed and time) and those that have not been traveled (the total distance to be moved by the moving point - those that have been traveled).

Special attention should be paid to the fact that when the moving point moves on the polyline, it is necessary to remove some parts of the line segment that has been traveled in order to correspond to the desired line segment; When the direction of movement of the represented line segment is different from that of the moving point, the similarity knowledge is generally used to find out and some line segments that can calculate the length and the direction is consistent with the direction of the desired line segment to seek the similarity ratio 2. Indefinite: This kind of moving point generally appears in conjunction with existential problems, that is, whether there is a point p that makes the problem satisfy some conclusions or when some conclusions exist, the position of the moving point p is found.

At this time, the solution can take the situation that the problem requires to be met as a condition of use, so that p is exactly where the requirements are met, and then combine the geometric knowledge to solve the problem, for example, when the problem requires the existence of a point p, so that the area of a triangle is 20. We need to first use the algebraic expression to represent the area of the triangle, and then make its value 20 In short, there are many types of moving points, and it is difficult to explain here. Pay more attention to the combination of algebraic simplification and geometric knowledge when solving problems, and you can slowly explore some of these rules.

The moving point of motion: This kind of moving point gives the direction of motion and the speed of motion, and we mainly represent the length of some line segments according to the specific speed of the motion Time = distance. According to the position of the moving point, the line segment can be divided into those that have been traveled (represented by speed and time) and those that have not been traveled (the total distance to be moved by the moving point - those that have been traveled).

There are bonus squares.

The root and the arithmetic square root have.

What are the differences and connections?

I'll answer with a reward.

Road. Let's talk about following and becoming the 15th fan for the first time.

Difference Between Square Root Answer and Arithmetic Square Root:

Definition of square root: If x = a, then x is the square root of a Definition of the arithmetic square root: The square root of a positive non-negative number is called its arithmetic square root, and in particular, the arithmetic square root of 0 is 0

The connection between the square root and the arithmetic square root:

The arithmetic square root is one of the square roots.

For example, 3 = 9, (-3) = 9, 3 and -3 are both square roots of 9, and 3 is the arithmetic square root of 9.

2) When the point p is moving on ab, what is the value of t, so that pb=bq?

t=43) Can point P catch up with point Q? If you can, find the value of t; If not, explain the reason for selling.

can catch up, t=12 because point p12 seconds can go from A to B, and at 12 cm to BC, just catch up with point Q.