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1 . 在空间直角坐标系中,点
关于
平面对称的点的坐标是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/664dcd44b22ab2dbf7d22f67e6c1e4d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d96461d2b3421aed548b754637ca8a.png)
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2024-02-12更新
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412次组卷
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3卷引用:上海市杨浦高级中学2023-2024学年高二下学期3月月考数学试卷
2 . 如图所示,以长方体
的顶点D为坐标原点,过D的三条棱所在的直线为坐标轴,建立空间直角坐标系,若
的坐标为
,则
的坐标为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d3aeafad20aa1777868b169b228ec3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d5b297c6bcf3520a7f372ef96a2038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053c0f6846f2bf8671b351a4263a0270.png)
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3 . 空间直角坐标系中,三个坐标平面将空间分为__________ 个部分.
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解题方法
4 . 如图,在四棱锥
中,
平面
,底面
是矩形,
,
,
是
上的点,直线
与平面
所成的角是
,则
的长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e20837a66df1185d5fbed39060e8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78e7c0d7e49c2025a68fd71fb6a661bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37793a3a810e823e10c340986f55ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e2fd1d179d6533a26734ea393eebc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
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5 . 在空间直角坐标系中,点
到
平面的距离为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdff2021d5e0a4cbbbfaff6d0499169f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
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6 . 在空间直角坐标系中,点
关于
平面的对称点的坐标为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10cf8d3369477b047830fca8e572ed7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d96461d2b3421aed548b754637ca8a.png)
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解题方法
7 . 有很多立体图形都体现了数学的对称美,其中半正多面体是由两种或两种以上的正多边形围成的多面体,半正多面体因其最早由阿基米德研究发现,故也被称作阿基米德体.如图,这是一个棱数为
,棱长都相等的半正多面体,它的所有顶点都在同一个正方体的表面上,可以看成是由一个正方体截去八个一样的四面体所得.已知点
为线段
上一点且
,若直线
与直线
所成角的余弦值为
,设半正多面体的棱长为
,将半正多面体补成正方体,建立如图所示的空间直角坐标系.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/f7c0b0c9-c673-425c-9dfc-2c6cfe7117e4.png?resizew=315)
(1)求正方体的棱长,并写出A,B,C,D,F点的坐标.
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e60fbe6820130fb20abc555a94b5ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d03acb29a5812acad760d564d6c84be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01eacbc4d1b4694985214023faa00128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/f7c0b0c9-c673-425c-9dfc-2c6cfe7117e4.png?resizew=315)
(1)求正方体的棱长,并写出A,B,C,D,F点的坐标.
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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8 . 在空间直角坐标系
中给定点
,则该点关于坐标平面
的对称点
的坐标为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/031121d8adbe9bb6d21190f9204f8cbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee6765a83140d745a6de4c85d9b6b50.png)
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解题方法
9 . 瀑布(图1)是埃舍尔为人所知的作品.画面两座高塔各有一个几何体,左塔上方是著名的“三立方体合体”(图2).在棱长为2的正方体
中建立如图3所示的空间直角坐标系(原点O为该正方体的中心,x,y,
轴均垂直该正方体的面),将该正方体分别绕着x轴,y轴,
轴旋转45°,得到三个正方体
,
(图4,5,6)结合在一起便可得到一个高度对称的“三立方体合体”(图7).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/28/e3b361ab-bbcd-4ec1-8d7e-a51250337d2a.png?resizew=324)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/28/0bb32dad-7e15-4145-bd9e-7b88d7c08cd4.png?resizew=666)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/28/cbcb0d91-53de-4cc9-8883-d5af9ffe1571.png?resizew=486)
(1)设
,求
,
.
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ecd73870da15600dfdc2220693fd81b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/750335e0a1896eb270407e86335a85a2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/28/e3b361ab-bbcd-4ec1-8d7e-a51250337d2a.png?resizew=324)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/28/0bb32dad-7e15-4145-bd9e-7b88d7c08cd4.png?resizew=666)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/28/cbcb0d91-53de-4cc9-8883-d5af9ffe1571.png?resizew=486)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb7fd30eee48d581e5d812c2e10aa11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fabf4c9a84e0b9690c7248a6f733f38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/750335e0a1896eb270407e86335a85a2.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c61c8e532d25d239382c40490905e7.png)
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10 . 已知
,则
的中点关于平面
的对称点的坐标是___
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/999caf873545f0de66131e29571d0e26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
您最近一年使用:0次