若A、B为直线a同旁的两点,则A(B)关于a的对称点A′(B′)与B(A)的连线段A′B(B′A)和a的交点为C,那么C点到A、B距离的和最小。这一性质为一类解析几何问题和函数的最值问题提供了极为简捷的方法。兹举例说明。例1 已知a(2,3),B(4,5),在y轴上找一点P,使|PA|+|PB|最小。 If A and B are two points adjacent to the line a, then A(B) points of intersection between the symmetry point A′(B′) of a and the connecting line segments A′B(B′A) and a of B(A). For C, then the sum of distances from point C to A, B is the smallest. This property provides an extremely simple method for parsing geometry problems and function-value problems. Here is an example. Example 1 Given a(2,3), B(4,5), find a point P on the y-axis to minimize |PA|+|PB|.