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一、结论 (1)点(a,b)关于直线x-y+m =0的对称点为(b-m,a+m); (2)点(a,b)关于直线x+y+m=0的对 称点为(-b-m,-a-m). 二、解释 将方程中的x代为a解出y即 为对称点纵坐标,将方程中的y代为b解出x 即为对称点横坐标.这两个结论在解题时可直 接使用,但许多同学只是记住结论并使用,对 其几何意义并不了解,因此觉得非常抽象.下 面给出结论(1)的几何解释,对于结论(2)可模 仿解决.
I. Conclusions (1) Points (a, b) Symmetric points about the straight line x-y+m =0 are (bm, a+m); (2) Points (a, b) about the straight line x+y+m= The symmetry point of 0 is (-bm,-am). Second, the explanation is to solve x in the equation for a and solve y for symmetry point ordinate. The y in the equation is b to solve x and it is the symmetry point abscissa. These two conclusions can be used directly when solving a problem, but many students just remember the conclusion and use it, they do not understand the geometric meaning, and therefore feel very abstract. The following gives the geometric interpretation of the conclusion (1), for the conclusion (2) ) Can imitate the solution.