Position relation on the number axis

The number axis is a straight line composed of infinite points, which is used to express the size and position relationship of numbers.

1, the relative size of the number

On the number axis, the more right the number is, the greater the value is; The farther to the left of the number, the smaller the value. We can compare the relationship between two numbers by counting axes. For example, on the number axis, the positional relationship between 2 and 5 is that 2 is to the left of 5, so 2 is less than 5.

2. Absolute value of numbers

The absolute value of a number is the distance from the origin, that is, the distance between the position of the number and the origin. Absolute value can represent the size of a number, whether it is positive or negative. For example, the absolute values of -3 and 3 on the number axis are all 3, because their distances from the origin are the same.

3, the reciprocal of the number

The inverse of a number refers to a number that is symmetrical about the origin on the number axis. For example, on the number axis, -2 and 2 are opposite to each other because they are at the same distance from the origin, but in opposite directions.

Position relation in plane rectangular coordinate system

In the plane rectangular coordinate system, we can use coordinates to represent the position of points. Coordinates are composed of abscissa and ordinate, which respectively represent the position of a point on the X axis and Y axis.

1, the position of the point

In the plane rectangular coordinate system, the position of a point is determined by its coordinates. For example, the coordinate of point A is (2,3), which means that its position on the X axis is 2 and its position on the Y axis is 3.

2. Symmetry of points

In the plane rectangular coordinate system, a point has certain rules about the coordinates of the origin, X axis and Y axis symmetry point. For example, the symmetry point of point A (-2,3) relative to the origin is a' (2,3), the axisymmetrical point of X is a (-2,3), and the axisymmetrical point of Y is a' (2,3).

3. Distance between two points

In the plane rectangular coordinate system, we can use Pythagorean theorem to calculate the distance between two points. For example, the distance from point A (2,3) to point B (5,7) is √[(5-2)? +(7-3)? ] = √[9+ 16]=√25=5。

Position relation in spatial rectangular coordinate system

In the space rectangular coordinate system, we can use coordinates to represent the position of points.

1, the position of the point

In the spatial rectangular coordinate system, the position of a point is determined by its coordinates. For example, the coordinate of point A is (2, 3, 4), which means that its position on the X axis is 2, its position on the Y axis is 3, and its position on the Z axis is 4.

2. Symmetry of points

In the spatial rectangular coordinate system, there are certain rules about the coordinates of points that are symmetrical about the origin, X axis, Y axis and Z axis. For example, the symmetry point of point A (-2, 3, 4) about the origin is A' (2, 3, 4), the axisymmetrical point of X is A(-2, 3, 4), the axisymmetrical point of Y is A'(2, -3, -4), and the axisymmetrical point of Z is a (-2, 3, 4).