如图,牧童在A处放牛,牧童家在B处,A、B处相距河岸的距离AC、BD分别为500m和300m,且C、D两处的距离为600m,天黑前牧童从A处将牛牵到河边去饮水,再赶回家,那么牧童最少要走_米?

问题描述:

如图,牧童在A处放牛,牧童家在B处,A、B处相距河岸的距离AC、BD分别为500m和300m,且C、D两处的距离为600m,天黑前牧童从A处将牛牵到河边去饮水,再赶回家,那么牧童最少要走______米?

作点A关于CD的对称点A′,连接A′B,则A′B的长即为AP+BP的最小值,过点B作BE⊥AC,垂足为E,∵CD=600m,BD=300m,AC=500m,∴A′C=AC=500m,CE=BD=300m,CD=BE=600m,∴A′E=A′C+CE=500+300=800m,在Rt△A′EB中,...