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解几中的有关对称问题,课本中没有给出系统内容,但解题中又经常用到,本文将结合图形,根据对称特点,找出规律,予以总结.1.“点关于点”的对称.点 P(x_1,y_1)关于 M(x_0,y_0)的对称点 P 的坐标,可由中点坐标公式得出:P′(2x_0-x_1,2y_0-y_1).2.“点关于直线”的对称直线 l 外一点 P(m,n)关于直线.:Ax+By+C=0(A,B 不同时为零)的对称点 P′的坐标,可利用 PP′与 l 的位置关系——l 垂直且平分 PP′求得,实际上是转化为“点关于点”的对
Solving the symmetry problem in several texts, the textbook content is not given in the textbook, but it is often used in the problem solving. This article will combine the graph, according to the characteristics of symmetry, find the law and summarize it. 1. The “point-to-point” symmetry Point P (x_1, y_1) The coordinates of the symmetry point P of M(x_0, y_0) can be derived from the midpoint coordinate formula: P′(2x_0-x_1, 2y_0-y_1).2. “Point about line” A coordinate P(m,n) outside a symmetric line l with respect to a straight line: Ax+By+C=0 (A, B are not zero at the same time) is the coordinate of the point of symmetry P′, and the positional relationship between PP′ and l can be used. l Vertically and evenly dividing PP’ is actually converted to “point-to-point”