真题
解题方法
1 . 在平面直角坐标系
中,将从点
出发沿纵、横方向到达点
的任一路径称为
到
的一条“
路径”.如图所示的路径
与路径
都是
到
的“
路径”.某地有三个新建居民区,分别位于平面
内三点
,
,
处.现计划在
轴上方区域(包含
轴)内的某一点
处修建一个文化中心.
(1)写出点
到居民区
的“
路径”长度最小值的表达式(不要求证明);
(2)若以原点
为圆心,半径为1的圆的内部是保护区,“
路径”不能进入保护区,请确定点
的位置,使其到三个居民区的“
路径”长度之和最小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/345e255af992e57179b2220149aca713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8d2f4252e18e728103bd4aea136e3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71962bc9eb657298a5ca4f0e346ce197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13063d4ce8e6dc59284b54925f41dd1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89cedf0d0fd7968770366824e4fb3147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)写出点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
(2)若以原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/7179c7d5-bd7a-4535-ae1d-908fd8a30b67.png?resizew=173)
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