The positional relationship between two straight lines on a plane: intersection and parallelism.
The intersection of two lines will produce the opposite vertex angle and the adjacent complementary angle.
The nature of antipodal angle: antipodal angle is equal.
The properties of adjacent complementary angles: zero complementary angles.
There is a special case where two straight lines intersect, and that is vertical.
The nature of the vertical line is: 1: the longest section of the vertical line.
2. One point, there is only one straight line, you should know the straight line.
This line is vertical.
Concept of parallel line: 1: There is only one point outside the straight line in the same plane.
The straight line is parallel to the known straight line.
2: Two lines parallel to the same line are parallel.
Properties of parallel lines: 1: Two straight lines are parallel at the same angle.
2. The internal dislocation angles are equal and the two straight lines are parallel.
3. The internal angles on the same side are complementary and the two straight lines are parallel.
4. Two straight lines are parallel and have the same angle.
5. The two straight lines are parallel and the internal dislocation angles are equal.
6. Two straight lines are parallel and complementary.
definition
The two number axes are perpendicular to each other and have a common origin, forming a plane rectangular coordinate system, which is called rectangular coordinate system for short.
Mathematical plane rectangular coordinate system
The concept of plane rectangular coordinate system;
Draw two axes that are perpendicular to each other and have a common origin on the plane. In this way, we say that the plane rectangular coordinate system is established on the plane, which is called rectangular coordinate system for short. The plane rectangular coordinate system has two coordinate axes, of which the horizontal axis is X-ASIS and the right direction is positive. The vertical axis is the Y(Y(Y-asis) axis, and the direction is positive. The plane where the coordinate system is located is called the coordinate plane, and the common origin of the two coordinate axes is called the origin of the plane rectangular coordinate system. X-axis and Y-axis divide the coordinate plane into four quadrants, the upper right quadrant is called the first quadrant, and the other three parts are called the second quadrant, the third quadrant and the fourth quadrant in turn counterclockwise. Quadrants are bounded by the number axis, and the points and origins on the horizontal and vertical axes do not belong to any quadrant. Generally speaking, the X axis and the Y axis take the same unit length.
Coordinates of the point:
After establishing the plane rectangular coordinate system, we can determine the coordinates of any point on the coordinate system plane. Conversely, for any coordinate, (we can determine a point it represents on the coordinate plane.
For any point C on the plane, the intersection point C is perpendicular to the X-axis and Y-axis respectively, and the corresponding points A and B perpendicular to the X-axis and Y-axis are called the abscissa and ordinate of the point C respectively, and the ordered pair (A, B) is called the coordinate of the point C. ..
A point is in different quadrants or coordinate axes, and its coordinates are different.
Coordinate characteristics of special position points:
The ordinate of the point on the 1.x axis is zero; The abscissa of a point on the y axis is zero.
2. The horizontal and vertical coordinates 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 connecting line of 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;
Characteristics of symmetrical points in plane rectangular coordinate system;
1. The coordinates of points symmetrical about X have the same abscissa and the opposite ordinate.
2. Regarding the coordinates of Y-symmetric points, the ordinate is the same, and the abscissa is the opposite number.
With regard to the coordinates of a point whose origin is central symmetry, the abscissa and abscissa are reciprocal, and the ordinate and ordinate are reciprocal.
The law of points and coordinates on each quadrant and coordinate axis;
The first quadrant: (+,+)
The second quadrant: (-,+)
The third quadrant: (-,-)
The fourth quadrant: (+,-)
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 this point on the X axis is 0, and the abscissa of the Y axis is 0.
Application of plane rectangular coordinate system
Determine the coordinate system of the plane position of the ground point on the projection plane by using the principle of rectangular coordinates;
Different from the rectangular coordinate system in mathematics, its horizontal axis is X axis and its vertical axis is Y axis. On the projection plane, the rectangular coordinate system with the projection of the central meridian as the axis adjustment, the equatorial projection as the horizontal axis (Y axis) and their intersection as the origin is called the national coordinate system, otherwise it is called the independent coordinate system.
Simple application of coordinate method;
1. Use coordinates to indicate geographical location.
2. Coordinate translation.
I studied Hebei Education Edition, and I don't know what a plane rectangular coordinate system is. The summary of the east plane rectangular coordinate system was copied from the encyclopedia.