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题目

Find the coordinates of symmetric points about

  (1) Each coordinate plane;  (2) Each coordinate axis;  

  (3) Coordinate origin

解析

Solution: According to the concepts of space rectangular coordinate system and symmetry points , we have

  (1)Regarding the coordinates of the symmetry point of the coordinate plane, you only need to change one of the original coordinates to the opposite number so that the line connecting the two symmetry points is perpendicular to the coordinate plane. The symmetry points of point with respect to planes , , and are:

, , .

  (2)The symmetry points of each coordinate axis can be regarded as the result of continuous symmetry transformation of the two coordinate planes. According to the result of (1), at this time, two of the original three coordinates must be changed to the opposite Number, the symmetry points of point about , , and axes are:

, , .

  (3)For the coordinates of the symmetry point about the origin, the three numbers of the original coordinates must be changed to their opposite numbers. The coordinates of the symmetry point about the origin are:

.

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