初中《几何》课本上的一道题.如图1,要在河边修建一个水泵站,分别向张庄、李庄送水.修在什么地方,可使所用水管最短? 课本的处理方法是将它转化为一道几何作图题: 已知:直线α和α的同侧两点A、B(图1).求作:点C,使C在直线α上,并且AC+CB最小. 作法 1. 作点A关于直线α的对称点A’. 2.连结A＇B交α于点C,点C就是所求的点. A problem in the junior high school “geometry” textbook. As shown in figure 1, a water pumping station should be built on the river to deliver water to Zhangzhuang and Lizhuang respectively. Where is the repaired water pipe and the shortest water pipe? Converted to a geometric drawing problem: Known: the two sides of the same line α and α of the straight line α and A (Figure 1). To achieve: point C, so that C is on the line α, and AC + CB minimum. Practice 1. Let point A be the symmetry point A’ of the straight line α. 2. Connect A’B to cross α at point C, and point C is the desired point.