1 . 定义:平面上一点到图形的最短距离为d,如图,OP=2,正方形ABCD的边长为2,O为正方形中心,当正方形ABCD绕O旋转时,d的取值范围是_________ .
![](https://img.xkw.com/dksih/QBM/2021/7/14/2763908997570560/2796512609116160/STEM/e7cddea6-b7a7-4859-80bf-75f4bee1870a.png?resizew=125)
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2021-08-29更新
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4卷引用:江西省景德镇一中2020-2021学年八年级下学期期末数学试题
江西省景德镇一中2020-2021学年八年级下学期期末数学试题(已下线)2023年河南省商丘市中考一模数学试题变式题11-15题重庆市北碚区朝阳中学2022-2023学年八年级下学期5月月考数学试题(已下线)专题23.12 旋转(全章分层练习)(基础练)-2023-2024学年九年级数学上册基础知识专项突破讲与练(人教版)
2 . 如图,在平面直角坐标系中,四边形
为正方形,点A的坐标
,
,则点C的坐标为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f48e1c656aace41360467f254e359d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a9b5996067a3fc9adcf0ca178dddf03.png)
![](https://img.xkw.com/dksih/QBM/2021/8/17/2788018419990528/2791061744402432/STEM/de01bc45-0dd8-4fea-aca7-1db4480f2742.png)
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3 . 如图所示,在平面直角坐标系中,正方形OABC的顶点O与原点重合,顶点A,C分别在x轴、y轴上,双曲线
(k≠0,x>0)经过AB、BC的中点N、F,连接ON、OF、NF.若S△BFN=3,则k=__ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07854693dd2e33f66030d6106eb6e0ee.png)
![](https://img.xkw.com/dksih/QBM/2021/6/12/2741598884167680/2789665324171264/STEM/704ccc85d17b4f81a6312927cff54eed.png?resizew=145)
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2021-08-19更新
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2卷引用:四川省成都市金牛区2020-2021学年九年级上学期期末数学试题
4 . 如图,在
中,
,
,正方形
的顶点
、
分别在
、
上,顶点
,
在
内,
,
,则点
到
的距离为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8b65efe27c217040c135d9e3111aee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ebb33adb2310a6e03918761e68204a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2257da1e2425f2ea9ac7440f52659ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b67af15119ea3075e16189c0fb51323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b20cd1a43264e4533d4980c99fdad4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2021/8/16/2787664375365632/2788616925478912/STEM/cd6559ae-c7fe-4d52-bfff-6f0f41c2bf85.png?resizew=133)
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5 . 如图,以
为边,在
的同侧分别作正方形
和等边
,连接
,延长
交
于点
,则
的度数是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2ee75a234ac05a3225e49ddd8c5065.png)
![](https://img.xkw.com/dksih/QBM/2021/8/16/2787460987609088/2788615340441600/STEM/852fefb5-e243-4552-8a41-2932274f0594.png?resizew=106)
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6 . 如图,在正方形ABCD中,点E、F、G分别是AD、DC、BC的中点,AF与DG交于点O,连接OE、OB.下列结论:①AF⊥DG;②BC=2OE;③AB=BO;④∠AOB=∠DGC;⑤∠OED=∠ABO.其中正确的结论有________ .(请填写序号)
![](https://img.xkw.com/dksih/QBM/2021/7/23/2770471309172736/2781846932291584/STEM/2d2fbaceda1f4cb6ab24778b6541eed3.png?resizew=149)
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7 . 如图,在Rt△ABC中,∠ACB=90°,∠A=45°,AB=4cm,点P从点A出发,以2cm/s的速度沿边AB向终点B运动(到点B时停止).过点P作PQ⊥AB交折线ACB于点Q,D为PQ中点,以DQ为边向右侧作正方形DEFQ.设点P的运动时间为x(s).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/00dace97-4701-4671-97d5-c1a9679a15bd.png?resizew=384)
(1)当点Q在边AC上时,正方形DEFQ的边长为__ cm(用含x的代数式表示);
(2)当点F落在边BC上时,x的值为__ ;
(3)当边BC的中点落在正方形DEFQ内部时,x的取值范围为__ .
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/00dace97-4701-4671-97d5-c1a9679a15bd.png?resizew=384)
(1)当点Q在边AC上时,正方形DEFQ的边长为
(2)当点F落在边BC上时,x的值为
(3)当边BC的中点落在正方形DEFQ内部时,x的取值范围为
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2021-08-14更新
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2卷引用:河北省沧州市孟村回族自治县2020-2021学年八年级下学期期末数学试题
解题方法
8 . 如图,在正方形
中,
.
为对角线
的延长线上一点,
为线段
的中点,
,连接
.已知
,下列说法正确的是______ .(将正确答案的序号填写下来)
①
;②
;③
;④
;⑤若
点为线段
上一动点,当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb91cb9a5a14169845d700fbd95890ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe31cb2315de7a5300d3efae202e2b6.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b2f883a2a2e0ccc5089fa9f0661e340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/793e03b60fc5ac445d6d44c508e7e73e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9d7b185c499b6bd81f57121f59fb930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ced64b8555b7f3a08faff110c4d15b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d09f17b41174377702f70bc27d10c95a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9ea44e59b1b5f61a5889790cc29d3d.png)
![](https://img.xkw.com/dksih/QBM/2021/5/10/2718155754766336/2786106582319104/STEM/f249101a-e59b-4306-884f-eae978514cce.png)
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9 . 如图所示的点阵中,相邻的四个点构成正方形,正方形的边长为1,则阴影部分的面积为 __________________ .
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/d3bdb5fc-c89d-4306-a7f6-b16730048fbd.png?resizew=109)
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10 . 将图1中的菱形沿对角线裁剪分成的四个三角形无重叠地拼成如图2所示的正方形.若拼成后的大正方形面积比菱形的面积大2,则菱形较长对角线与较短对角线的差为__________ .
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/13/1c6389a9-4744-4b8a-aa9f-4135271bd060.png?resizew=249)
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