1 . 在平面直角坐标系中,定义
为两点
、
的“切比雪夫距离”,又设点
及
上任意一点
,称
的最小值为点
到直线
的“切比雪夫距离”,记作
,给出下列四个命题,正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32a7ccf5858c4bee028cd4f0c7a8537f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32286c3865f06865920816e7685c497a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87ab04028bf648fbb8c9296acdeaaf5a.png)
A.对任意三点![]() ![]() |
B.已知点![]() ![]() ![]() |
C.到定点![]() ![]() |
D.定点![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-06-25更新
|
985次组卷
|
4卷引用:福建省厦门第一中学2022-2023学年高三五模数学试题
名校
解题方法
2 . 在平面直角坐标系中,两点
、
的“曼哈顿距离”定义为
,记为
,如点
、
的“曼哈顿距离”为9,记为
.
(1)点
,
是满足
的动点
的集合,求点集
所占区域的面积;
(2)动点
在直线
上,动点
在函数
图像上,求
的最小值;
(3)动点
在函数
的图像上,点
,
的最大值记为
,请选择下列二问中的一问,做出解答:
①求证:不存在实数
、
,使
;
②求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84bd36d19352628cb54c214436ee3322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27bd43bc4af1e3b28d0de0cc561b879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c59185f3d9547cd9065d10dcbb4127d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e66b64267481405cc49dad9d8916c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9404ad60dd25cb0df6c37032d50b72ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dafabc98a78486af4fbf346e7cfad11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bd35a290bbcf999ec26930c747084b.png)
(1)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9404ad60dd25cb0df6c37032d50b72ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7bce4bf9358998e26ff0715c909a19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(2)动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ea05a2396e436b4df62d6328dbeaddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e66b64267481405cc49dad9d8916c7.png)
(3)动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c064084f6326c8b994c2bcb80ad258da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae4a30a3210d0a8130d5a1183289c23f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e66b64267481405cc49dad9d8916c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6d8a4cf957865fad1cb648fcd2cbaa0.png)
①求证:不存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d41cfe4280d2384c9dd4287c8f07954.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6d8a4cf957865fad1cb648fcd2cbaa0.png)
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