I. Objectives and requirements
1. Solve the application significance of ordered number pairs and understand the common methods of determining points on the plane.
2. Cultivate students' awareness of using mathematics and stimulate students' interest in learning.
3. Grasp the relationship between coordinate change and graphic translation; Can use the translation law of points to translate plane graphics; According to the change of coordinates of each point on the graph, the moving process of the graph is judged.
4. Cultivate students' thinking ability in images and the consciousness of combining numbers with shapes.
5. Coordinate representation translation embodies the application of plane rectangular coordinate system in mathematics.
Second, the main points
Master the relationship between coordinate transformation and graphic translation;
Ordered number pairs and the method of determining points on the plane.
Third, difficulties.
Using the relationship between coordinate transformation and graphic translation to solve practical problems;
Use ordered number pairs to represent points on the plane.
Fourth, the knowledge framework.
Verb (abbreviation of verb) summary of knowledge points and concepts
1. Ordered number pair: a word containing two numbers represents a definite position, where each number represents a different meaning. We call this number pair consisting of two numbers A and B in the order of (A, B) (A, B), where A stands for the horizontal axis and B stands for the vertical axis.
2. Plane rectangular coordinate system: Two number axes perpendicular to each other on the same plane and having a common origin form a plane rectangular coordinate system, which is called rectangular coordinate system for short. Usually, the two number axes are placed in horizontal and vertical positions respectively, and the right and upward directions are the positive directions of the two number axes respectively. The horizontal axis is called X axis or horizontal axis, the vertical axis is called Y axis or vertical axis, and the X axis or Y axis is collectively called coordinate axis. Their common origin O is called the origin of rectangular coordinate system.
3. Horizontal axis, vertical axis and origin: the horizontal axis is called X axis or horizontal axis; The vertical axis is called Y axis or vertical axis; The intersection of the two coordinate axes is the origin of the plane rectangular coordinate system.
4. Coordinates: For any point P on the plane, the passing P is perpendicular to the X axis and Y axis respectively, and the vertical foot is on the X axis and Y axis respectively. The corresponding numbers a and b are called the abscissa and ordinate of the point p, respectively.
5. Quadrant: Two coordinate axes divide the plane into four parts, the upper right part is called the first quadrant, and the counterclockwise part is called the second quadrant, the third quadrant and the fourth quadrant. The point on the coordinate axis is not in any quadrant.
6. Coordinate characteristics of special location points
(1) The ordinate of the point on the x axis is zero; The abscissa of a point on the y axis is zero.
(2) The abscissa and ordinate of the points on the bisector of the first quadrant and the third quadrant are equal; The horizontal and vertical coordinates of the points on the bisector of the second and fourth quadrants are opposite to each other.
(3) If the abscissas of any two points are the same, the line connecting the two points is parallel to the longitudinal axis; If the vertical coordinates of two points are the same, the straight line connecting the two points is parallel to the horizontal axis.
(4) Distance from point to axis and origin.
The distance from the point to the X axis is | y | The distance from the point to the Y axis is | x | The distance from the point to the origin is the square of x plus the square of y and then open the root sign;
7. Characteristics of symmetrical points in plane rectangular coordinate system
(1) The coordinates of points that are symmetrical about the X axis have the same abscissa and the opposite ordinate. (horizontal and vertical)
(2) With regard to the coordinates of Y-symmetric points, the ordinate is the same and the abscissa is the opposite number. (horizontal and vertical)
(3) With regard to the coordinates of a point whose origin center is symmetrical, the abscissa and the ordinate are reciprocal, and the ordinate and the ordinate are reciprocal. (Horizontal and vertical directions)
8. The law of points and coordinates on each quadrant and coordinate axis
The first quadrant: (+,+) is positive.
The second quadrant: (-,+) negative and positive
The third quadrant: (-,-) negative.
The fourth quadrant: (+,-) plus or minus
Positive direction of X axis: (+,0)
Negative direction of X axis: (-,0)
Positive direction of Y axis: (0,+)
Negative direction of Y axis: (0,-)
The ordinate of the point on the X axis is 0, and the abscissa of the point on the Y axis is 0.
Origin: (0,0)
Note: Points in the coordinate system in the form of pairs (x, y) (e.g. 2, -4), where "2" is the x-axis coordinate and "-4" is the y-axis coordinate.
9. Simple application of coordinate method:
(1) The geographical position is expressed in coordinates.
(2) coordinate translation.
10. Other formulas of plane rectangular coordinate system
Points on the (1) coordinate plane correspond to ordered real numbers one by one.
(2) The horizontal and vertical coordinates of each point on the bisector of the three-quadrant angle are equal.
(3) The abscissa and ordinate of each point on the bisector of the 24-quadrant angle are opposite.
(4) Move up and down a little, and the abscissa remains unchanged, that is, the abscissa of the point on the straight line parallel to the Y axis remains unchanged.
(5) Points on the Y axis, with the abscissa of 0.
(6) The point on the X axis with the ordinate of 0.
(7) The points on the coordinate axis do not belong to any quadrant.
Six, the classic example
Example 1 A robot starts from point O, walks 3 meters due east to reach point A 1, walks 6 meters due north to reach point A2, walks 9 meters due west to reach point A3, walks 12 meters due south to reach point A4, and walks 15 meters due east to reach point A5. If A65438+,
Example 2 is a small flag pattern painted on a square paper. If point A is represented by (0,0) and point B by (0,4), the position of point C can be represented by ().
a 、( 0，3) B 、( 2，3) C 、( 3，2) D 、( 3，0)
Example 3 As shown in Figure 2, according to the position of each point on the coordinate plane, write the coordinates of the following points:
a()，B()，C().
Example 4 translates △ABC with an area of 12cm2 to the position of △DEF in the positive direction of the X axis, and the corresponding coordinates are shown in the figure (A and B are constants).
(1), find the coordinates of point d and point e.
(2) Find the area of the quadrilateral.
Example 5 If two points A (3,4) and B (-2,4) are straight lines AB, then straight line AB ()
A, through the origin b, parallel to the y axis.
C, parallel to the X axis D, none of the above statements are correct.