Cartesian coordinates/Cartesian coordinates
1, a word containing two numbers indicates a definite position, where the two numbers each indicate a different meaning. We call this number pair composed of two numbers in sequence an ordered number pair, and write it as (a, b).
2. A point on the number axis can be represented by a number, which is called the coordinate of this point.
3. 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, in which the horizontal axis is the X axis and the right direction is the positive direction; The vertical axis is the y axis and the direction is the positive direction. 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.
4. Coordinate characteristics of special anchor 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.
5. 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 opposite ordinate.
2. Regarding the coordinates of Y-symmetric points, the ordinate is the same, and the abscissa is the opposite number.
3. With regard to the coordinates of a point whose origin center is symmetrical, 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: (+,-)
X axis positive direction: (+,0)x axis negative direction: (-,0)y axis positive direction: (0, +)y axis negative direction: (0,-)
The ordinate of this point on the X axis is 0, and the abscissa of the Y axis is 0.
Binary linear equations
(1) definition
Binary linear equation refers to an equation with two unknowns (such as X and Y), and the degree of the unknowns is 1. Two combined linear equations with two unknowns are called binary linear equations.
(2) The solution method of binary linear equation
① Substitution elimination method
② Method of addition, subtraction and elimination
Unequal and unequal groups
(1) inequality
Using inequality symbols (
(2) the essence of inequality
① symmetry;
② Transitivity;
③ monotonicity of addition, that is, additivity of inequality in the same direction;
④ Monotonicity of multiplication;
⑤ Multiplicity of positive inequality in the same direction;
⑥ Positive inequalities can be multiplied;
⑦ Positive inequalities can be squared;
(3) One-dimensional linear inequality
A formula connected by an inequality symbol contains an unknown number whose degree is 1, whose coefficient is not 0, and whose left and right sides are algebraic expressions is called one-dimensional linear inequality.
(4) One-dimensional linear inequalities
The group of one-dimensional linear inequalities consists of several one-dimensional linear inequalities with the same unknowns.
Intersecting line and parallel line
1. Among the four angles formed by the intersection of two straight lines, two adjacent angles are called adjacent complementary angles, which are characterized in that two angles * * * use one side and the other side is an opposite extension line, and the nature is that the adjacent complementary angles are complementary; Two diagonals are called diagonals, which are characterized in that their two sides are opposite extension lines. The property is that the vertex angles are equal.
2. Three-line octagon: opposite vertex angle (equal), adjacent complementary angle (complementary), congruent angle, internal dislocation angle and internal angle on the same side.
3. Two straight lines are cut by a third straight line:
Isomorphism angle f (on the same side of two straight lines and on the same side of the third straight line)
Internal dislocation angle z (inside two straight lines and both sides of the third straight line)
Inner angle of the same side u (in two straight lines, on the same side of the third straight line)
If one of the four angles formed by the intersection of two straight lines is 90 degrees, the two straight lines are said to be perpendicular to each other. One of the straight lines is called the perpendicular of the other straight line, and their intersection point is called the vertical foot.
5. Vertical three elements: vertical relationship, vertical sign and vertical foot.
6. Vertical axiom: There is one and only one straight line perpendicular to the known straight line.
7. The vertical segment is the shortest.
8. Distance from point to straight line: the length of the vertical section from a point outside the straight line to this straight line.
9. Parallelism axiom: After passing a point outside a straight line, there is one and only one straight line parallel to this straight line.
Inference: If two straight lines are parallel to the third straight line, then the two straight lines are also parallel to each other. If b//a, c//a, then b//c
10, determination of parallel lines:
(1) The same angle is equal, and two straight lines are parallel. 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.
1 1. Inference: If two straight lines are perpendicular to the same straight line in the same plane, then the two straight lines are parallel.
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★ Summary of unit knowledge points in the second volume of junior one mathematics.
★ Important knowledge points in the second volume of Grade One Mathematics
★ Summarize and sort out the math knowledge points in the second volume of Grade One.
★ Summary of knowledge points in the second volume of junior one mathematics.
★ Knowledge points in the second volume of Grade One Mathematics
★ Review the knowledge points in the second volume of seventh grade mathematics.
★ Summary of seventh grade mathematics knowledge points
★ Knowledge points in the second volume of seventh grade mathematics published by People's Education Edition
★ outline of knowledge points in the second volume of seventh grade mathematics
★ Summary of knowledge points in the second volume of Mathematics in the first day of the Soviet Education Edition