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在平面内,两次平移变换的最后结果相当于一次平移变换,同一旋转中心进行两次旋转变换的最后结果相当于一次旋转变换,如果两次旋转的旋转中心不同,这两次旋转变换的最后结果,还可以用一次旋转变换代替吗?对于这一问题,老师们进行了讨论,研究方法是作图,发现:一个图形经过旋转中心不同的两次旋转,旋转后的图形与原图形对应点连线的中垂线交于一点.如图1所示,图形经过旋转中心分别为O_1和O_2的两次旋转,可以用旋转中心为O的一次旋转来代替.由此得到结论:对于不同的旋转中心,接连进行两次旋转的最后结果,可以用一次旋转代替.
In the plane, the final result of two translational transformations is equivalent to one translation transformation. The final result of two rotation transformations in the same rotation center is equivalent to one rotation transformation. If the rotation centers of two rotation are different, the last two rotation transformations As a result, can we use a rotation transform instead? For this problem, the teachers discussed the method is to map and found: a graph through the rotation center of the two different rotation, the rotated graphics and the original graphics corresponding points As shown in Figure 1, the rotation of the figure through the rotation of O_1 and O_2, respectively, can be replaced by a rotation with a center of rotation of 0. It follows from this that for different Rotation center, the result of two consecutive rotations, you can use a rotation instead of.