1. Make clear how to establish a spatial rectangular coordinate system; Clear how to express any point in space;

Can find the coordinates of the point in the spatial rectangular coordinate system.

teaching process

First, autonomous learning.

1. How to establish a plane rectangular coordinate system, how to determine the coordinates of points, and how to express them?

2. How to represent a point on a plane? In space?

3. Coordinate solutions of some symmetrical points.

A point symmetrical about the coordinate plane;

A point symmetrical about the coordinate plane;

A point symmetrical about the coordinate plane;

On axisymmetric problems;

On the point of axial symmetry;

On axisymmetric problems;

Second, teacher-student interaction

Example 1 Write four-point coordinates in a cuboid.

Discussion: If the point is the origin and the ray direction is the axis, what are the coordinates of each vertex?

Variant: Known, track its position in space.

Example 2 is a regular quadrangular pyramid with a middle bottom. If so, try to establish a spatial rectangular coordinate system and determine the coordinates of each vertex.

Exercise 1. Establish an appropriate rectangular coordinate system and determine the vertex coordinates of a regular tetrahedron with a length of 3.

Exercise 2. It is known that it is a cube with a length of 2, and the length is the midpoint of sum. Establish a suitable rectangular coordinate system in space and try to write the coordinates of each midpoint in the diagram.

Third, consolidate the practice.

1. The correct statement about spatial rectangular coordinate system is ().

The positions in are interchangeable.

There is a one-to-one correspondence between points in B rectangular coordinate system and ternary ordered array.

The three coordinate axes in the rectangular coordinate system divide the space into eight parts.

D the coordinate position of a point in different rectangular coordinate systems can be the same.

2. If the point is known, the coordinate of the point about the origin symmetry point is ().

A.B. C. D。

3. If the coordinates of the three vertices are known as, then the coordinates of the center of gravity are ().

A.B. C. D。

4. It is called a parallelogram, and the coordinates of the vertices.

5. The geometric meaning of the equation is.

Fourth, after-class reflection

Five, after-school consolidation exercises

1. In the spatial rectangular coordinate system, for a given point, find the coordinates of its symmetrical point about the coordinate plane, coordinate axis and origin respectively.

2. Set a cuboid whose length, width and height are the midpoint of the line segment. Taking a straight line as the axis, the axis and the axis respectively establish a spatial rectangular coordinate system.

(1) Find the coordinates;

(2) coordinates;