【初二初三必读】 线段最值探索 (上) —— 斜大于直
通常,我们把直线外一点到这条直线的垂线段的长度叫做点到直线的距离。经过探究我们得到一个事实:直线外一点与直线上各点连接的所有线段中,垂线段最短。即我们今天所要讲的内容“斜大于直”问题。
“斜大于直”问题在中考线段最值中考察较为广泛,即点到线的最短距离问题,常见的有单线段的最值,线段和的最小,系数不为1的线段和的最值(胡不归问题)等等。如需加深难度通常将定点和定线隐藏处理即可。本文将通过7大变式予以说明。
![](http://pic.ikafan.com/imgp/L3Byb3h5L2h0dHBzL2ltYWdlMTA5LjM2MGRvYy5jbi9Eb3dubG9hZEltZy8yMDIxLzAzLzA4MTYvMjE3MTc5MTIxXzJfMjAyMTAzMDgwNDI3NTkxNzc=.jpg)
基本模型:点P到直线MN的最短距离为线段PA的长.
![](http://pic.ikafan.com/imgp/L3Byb3h5L2h0dHBzL2ltYWdlMTA5LjM2MGRvYy5jbi9Eb3dubG9hZEltZy8yMDIxLzAzLzA4MTYvMjE3MTc5MTIxXzNfMjAyMTAzMDgwNDI3NTkyNDA=.jpg)
例题精选
![](http://pic.ikafan.com/imgp/L3Byb3h5L2h0dHBzL2ltYWdlMTA5LjM2MGRvYy5jbi9Eb3dubG9hZEltZy8yMDIxLzAzLzA4MTYvMjE3MTc5MTIxXzRfMjAyMTAzMDgwNDI3NTkzMDI=.jpg)
![](http://pic.ikafan.com/imgp/L3Byb3h5L2h0dHBzL2ltYWdlMTA5LjM2MGRvYy5jbi9Eb3dubG9hZEltZy8yMDIxLzAzLzA4MTYvMjE3MTc5MTIxXzJfMjAyMTAzMDgwNDI3NTkxNzc=.jpg)
变式1:“隐点型”----(对称隐藏定点型)
![](http://pic.ikafan.com/imgp/L3Byb3h5L2h0dHBzL2ltYWdlMTA5LjM2MGRvYy5jbi9Eb3dubG9hZEltZy8yMDIxLzAzLzA4MTYvMjE3MTc5MTIxXzVfMjAyMTAzMDgwNDI3NTk0MTM=.jpg)
![](http://pic.ikafan.com/imgp/L3Byb3h5L2h0dHAvaW1hZ2UxMDkuMzYwZG9jLmNuL0Rvd25sb2FkSW1nLzIwMjEvMDMvMDgxNi8yMTcxNzkxMjFfNl8yMDIxMDMwODA0Mjc1OTUwNQ==.jpg)
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