构造直角三角形,求解最短距离

• 作 者: 徐华山
• 机 构: 江苏盐城大丰市第五中学,
• 出 处: 时代数学学习
• 发表日期: 2006年09期
• 关键词: 最短距离 最短路径 化归 最短路线 对称点 徐华山 展开方式 棱长 江苏盐城 上底

我们利用轴对称可将实际生活中的最短路线化归为两点间的线段.那么怎样求解这样的最短距离呢?这里关键是将问题中的已知线段通过平移与两点间的线段构成直角三角形,由此利用勾股定理求解.例1如图1,两个村子位于河流CD的同侧,它们到河流CD的距离分别为AC=1km,BD=3km,量得CD=3km;

We use axial symmetry to classify the shortest route in real life as a line between two points. How to solve such a shortest distance? The key here is to make the known line segment of the problem through the translation and the line segment between the two points constitute a right angle. Triangles, thus using the Pythagorean theorem to solve. Example 1 In Figure 1, the two villages are on the same side of the river CD, and their distance to the CD of the river is AC = 1km, BD = 3km, and CD = 3km;