如下图,要在街道旁修筑一个奶站,向居民区A、B提供牛奶,奶站应建在什么地方,才能使从A、B到它的距离之和最短?把这个实际问题转化为数学问题就是:如图1,A、B是直线a同侧的两点,试在a上求一点P,使PA+PB最小.解:如图1,作点A关于a的对称点A_1,连接A_1B交a于点P,则P就是所求的点.证明:设a上还有异于P点的另一点Q,连接PA、QA、QA_1、QB.因为直线a是AA_1的对称轴,P、Q在对称轴上, As shown below, a milk station should be built beside the street to supply milk to residential areas A and B. Where should the milk station be built so that the shortest distance from A and B to it? Turn this practical problem into mathematics. The problem is: Figure 1, A, B is two points on the same side of the line a, try to find a point P on a, so that the minimum PA + PB. Solution: Figure 1, for point A on the point of symmetry A_1, connect A_1B crosses a at point P, then P is the point sought. Proof: Let Q be another point Q different from point P, connecting PA, QA, QA_1, QB. Because line a is the axis of symmetry of AA_1, P Q is on the axis of symmetry.