利用对称变换,根据“两点之间线段最短”或“三角形任两边之和大于第三边”,常能解决线段和最短或不等问题,下面举例说明.例1已知直线l外有一定点P,试在l上求两点A、B,使AB=m(定长),且PA+PB最短.分析:当把P点沿l方向平移至C(如图1),使PC=m,那么问题就转化为在l上求一点B,使CB+P Using symmetry transformation, according to “the shortest line segment between two points” or “the sum of any two sides of the triangle is greater than the third edge”, the line segment and the shortest or unequal problems can often be solved. Here is an example. Example 1 There is a certain point outside the known line l. P, try to find two points A, B on l, so that AB = m (fixed length), and PA + PB shortest. Analysis: When the P point is translated in the direction of l to C (Figure 1), so that PC = m , then the problem is turned into a bit B on l, so that CB+P