2023九年级·全国·专题练习
解题方法
1 . 对于平面直角坐标系
中的图形
和图形
,给出如下定义:在图形
上存在两点
(点
可以重合),在图形
上存在两点
(点
可以重合)使得
,则称图形
和图形
满足限距关系.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/16/8922f3da-835b-4d76-8a21-15c0ac2b623d.png?resizew=395)
(1)如图1,点
,点
在线段
上运动(点
可以与点
重合),连接
.
①线段
的最小值为______,最大值为______;线段
的取值范围是______;
②在点
,点
中,点______与线段
满足限距关系;
(2)在(1)的条件下,如图2,
的半径为1,线段
与
轴、
轴正半轴分别交于点
,且
,若线段
与
满足限距关系,求点
横坐标的取值范围;
(3)
的半径为
,点
是
上的两个点,分别以
为圆心,2为半径作圆得到
和
,若对于任意点
,
和
都满足限距关系,直接写出r的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eaa137a2290a9a9ec7ad635d17dbb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eaa137a2290a9a9ec7ad635d17dbb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8021150f6a208a316d31cb8313e42b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eaa137a2290a9a9ec7ad635d17dbb6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/16/8922f3da-835b-4d76-8a21-15c0ac2b623d.png?resizew=395)
(1)如图1,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348d0426ecad004444d5ee2411c5c2d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662a33b9677e5a92e98cfd4fffcf4e3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d1c6e445036fcc20e5a5389aa0233e.png)
①线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
②在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
(2)在(1)的条件下,如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231c3e0c5366da20b9c8de0423e7a7d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32710f75858e15e2529c8d14f1758f04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e1b2d25e575038885c5eddf1ddb229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbe6f236537639afa08bd1d8440b89b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbe6f236537639afa08bd1d8440b89b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f3be3806ce3b7b636535b64c8db3fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9110c10c6b6abeb9021f59dd7852125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbe6f236537639afa08bd1d8440b89b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f3be3806ce3b7b636535b64c8db3fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9110c10c6b6abeb9021f59dd7852125.png)
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2 . 对于平面直角坐标系xOy中的图形
和图形
给出如下定义:在图形
上存在两点A,B(点A,B可以重合),在图形
上存在两点M,N(点M,N可以重合)使得
.则称图形
和图形
满足限距关系.
(1)如图,点
,
,
,点F在CE上运动(点F可以与C,E重合),连接OF,DF.
①线段OF的最小值为 ,最大值为 ;线段DF的取值范围是 ;
②在点O,D中,点 与线段CE满足限距关系;
![](https://img.xkw.com/dksih/QBM/2022/4/14/2965231858769920/2984349530431488/STEM/aa3e4d8a-b335-40e4-81c7-f49a87665951.png?resizew=258)
(2)如图,正方形ABMN的边长为2,直线PQ分别于x轴,y轴交于点Q,P,且与x轴正方向的夹角始终是
,若线段PQ与正方形ABMN满足限距关系,求点P的纵坐标
的取值范围;
![](https://img.xkw.com/dksih/QBM/2022/4/14/2965231858769920/2984349530431488/STEM/52e1179d-4e6b-425a-b613-029dff557288.png?resizew=240)
(3)如图,正方形ABMN的顶点均在坐标轴上,
,G,H是正方形边上两点,分别以G,H为中心作边长为1的正方形,与正方形ABMN的四边分别平行,若对于任意的点G,H,以G,H为中心的正方形都满足限距关系,直接写出b的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eaa137a2290a9a9ec7ad635d17dbb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eaa137a2290a9a9ec7ad635d17dbb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8021150f6a208a316d31cb8313e42b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eaa137a2290a9a9ec7ad635d17dbb6.png)
(1)如图,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37df9dad3961893b22d6639c4311e267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ff329f3b12cf5678e99941e7188621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c05cabb9b25ebeefc409daac605b480.png)
①线段OF的最小值为 ,最大值为 ;线段DF的取值范围是 ;
②在点O,D中,点 与线段CE满足限距关系;
![](https://img.xkw.com/dksih/QBM/2022/4/14/2965231858769920/2984349530431488/STEM/aa3e4d8a-b335-40e4-81c7-f49a87665951.png?resizew=258)
(2)如图,正方形ABMN的边长为2,直线PQ分别于x轴,y轴交于点Q,P,且与x轴正方向的夹角始终是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6ec1e326713ddcd6dd66a24a809bdb8.png)
![](https://img.xkw.com/dksih/QBM/2022/4/14/2965231858769920/2984349530431488/STEM/52e1179d-4e6b-425a-b613-029dff557288.png?resizew=240)
(3)如图,正方形ABMN的顶点均在坐标轴上,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/586d72e590dc177c12a5332b87655676.png)
![](https://img.xkw.com/dksih/QBM/2022/4/14/2965231858769920/2984349530431488/STEM/70aa18b6-c29f-4e8e-a9c5-5657573eb766.png?resizew=229)
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3 . 如图,
的顶点坐标分别为
,动点P、Q同时从点O出发,分别沿x轴正方向和y轴正方向运动,速度分别为每秒3个单位和每秒2个单位,点P到达点B时点P、Q同时停止运动.过点Q作
分别交
、
于点M、N,连接
、
.设运动时间为t(秒).
![](https://img.xkw.com/dksih/QBM/2021/6/21/2747526619070464/2747720210595840/STEM/1f57829e565b4854b9d51d00548f6bd5.png?resizew=183)
(1)求点M的坐标(用含t的式子表示);
(2)求四边形
面积的最大值或最小值;
(3)是否存在这样的直线l,总能平分四边形
的面积?如果存在,请求出直线l的解析式;如果不存在,请说明理由;
(4)连接
,当
时,求点N到
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fb1f3dc89d8e205d7996c7f6bade9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040836318648e2428e150f6b5b5891dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://img.xkw.com/dksih/QBM/2021/6/21/2747526619070464/2747720210595840/STEM/1f57829e565b4854b9d51d00548f6bd5.png?resizew=183)
(1)求点M的坐标(用含t的式子表示);
(2)求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a91c4c08a80b24a8068ae397b97521b7.png)
(3)是否存在这样的直线l,总能平分四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a91c4c08a80b24a8068ae397b97521b7.png)
(4)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e266f45b2189462b6ade21cf9177787c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
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2021-06-21更新
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5卷引用:湖南省衡阳市2021年中考数学真题
湖南省衡阳市2021年中考数学真题2022年浙江省宁波市鄞州蓝青学校九年级下学期期中数学试题2023年湖南省衡阳市西渡镇咸水中学中考一模数学试卷(已下线)专题11一次函数与几何压轴问题(优选真题44道)-学易金卷:三年(2021-2023)中考数学真题分项汇编【全国通用】(已下线)专题12 函数综合-学易金卷:三年(2021-2023)中考数学真题分项汇编(湖南专用)
4 . 阅读材料:
在平面直角坐标系
中,点
到直线
的距离公式为
.
例如:求点
到直线
的距离.
解:由直线
知,
,
,
,
∴点
到直线
的距离为
.
根据以上材料,解决下列问题:
问题1:点
到直线
的距离为__________;
问题2:已知
是以点
为圆心,1为半径的圆,
与直线
相切,求实数
的值;
问题3:如图,设点
为问题2中
上的任意一点,点
、
为直线
上的两点,且
请求出
的最大值和最小值.
在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f6e1f67dc15c3cf135a78af95c70fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf6a453276e622be852a764602a452ad.png)
例如:求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b48b1304928940d82f01c0a6ae80f55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5b6d902834937cf678992a391f4d4d.png)
解:由直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5b6d902834937cf678992a391f4d4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcdb7a488910743dc5c63afb394b87e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b724e955f78d88ce2ffce1e1ffb8a3ae.png)
∴点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b48b1304928940d82f01c0a6ae80f55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5b6d902834937cf678992a391f4d4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d23b34f1588cc53178239e08c2188ab.png)
根据以上材料,解决下列问题:
问题1:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2562cb077730502e65ea794cadd1755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21812d86742205189c3ff797a43b4161.png)
问题2:已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24dba5cc987db7f50f9b8e2d4544006d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cdc4824212e952b5a32d89187b8997a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
问题3:如图,设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3f999bcdcdc1b9d56e0639cadd96dbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbb48c435c1ea5452cd9c9dd05e53ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd1b3419a8941b4714c7e22507590e0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/25/c2915148-119e-404d-87ab-2c06ef06f4a8.png?resizew=180)
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|
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19卷引用:江苏省东台市第六联盟2018届九年级上学期期中考试数学试题
江苏省东台市第六联盟2018届九年级上学期期中考试数学试题(已下线)2年中考1年模拟 第三篇 函数 专题12 一次函数及其应用(已下线)2年中考1年模拟 第七篇 专题复习篇 专题37 阅读理解问题(已下线)决胜2018中考压轴题全揭秘 专题29 新定义和阅读理解型问题2017-2018学年中考数学经典题型训练卷:新定义阅读问题(已下线)决胜2018中考压轴题全揭秘 专题23 最值问题(已下线)决胜2018中考压轴题全揭秘 专题06 一次函数问题【全国百强校】宁夏银川市第二中学教育发展共同体初中学校2019届九年级下学期第一次模拟考试数学试题浙江省台州市第四协作区2019-2020学年九年级上学期10月月考数学试题贵州省遵义市赤水市2019-2020学年九年级上学期期中数学试题2019年内蒙古克什克腾旗九年级二模数学试题浙江省台州市书生中学2020-2021学年九年级上学期第一次月考数学试题浙江省台州市2020-2021学年第一学期九年级数学第一次月考试题人教版浙江省台州市双语中学2020-2021学年九年级上学期10月月考数学试题(已下线)【万唯原创】新运算学习型·满分专练(一)(已下线)【万唯原创】新运算学习型·基础专练(一)(已下线)【万唯原创】2017年山西中考数学-试题研究-第二部分题型3类型3浙江省台州市路桥区路桥实验中学2020-2021学年九年级上学期12月月考数学试题山东省济宁市微山县鲁桥镇第一中学2021-2022学年九年级上学期第二次学情调研数学试题
5 . 【知识探索】小华所在的数学兴趣小组在学习中发现有些含参直线存在恒过一点的现象,例如:直线
可以化作
,进而发现当
时,不论
为何值,总有
.故直线
恒过点
.
【迁移运用】已知点
,直线
,若点
到直线
的距离为
.则
的最大值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f897df38ca5342682ac056a50a9b4f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7ee89b62104e6a06d103fdbf2e0513c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba53065eb180a682305fddb95d14b62f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f897df38ca5342682ac056a50a9b4f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ed3636ebd750003453533da1463036b.png)
【迁移运用】已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e648aa381d4c1ee6639536b0b1510a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44bfcfc990b5d5dbb6d82f3c33799cc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
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名校
6 . (1)发现:如图1,点A为线段
外一动点,且
,
.则当点A位于______时,线段
的长取得最大值,且最大值是______.
(2)应用:点A为线段
外一动点,且
,
,如图2所示,分别以
,
为边作等边
和等边
,连接
、
,求出线段
长的最大值并说明理由
(3)拓展:如图3,在点A的正东方向3000米处有一物资补给站B,某园林部门要规划一片牡丹种植园
,要求
,
,且
米.为了在点A有最佳的观赏效果,要求线段
最长,试求线段
长的最大值及此时点C到直线
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)应用:点A为线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.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/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(3)拓展:如图3,在点A的正东方向3000米处有一物资补给站B,某园林部门要规划一片牡丹种植园
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a651eb577dbada1f29590e558d6f9fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3bbe4cdd2c154bd9a8073b0d4cecb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e7dccc5222820f20ddf2d3561bb1993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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7 . 在平面直角坐标系中,坐标原点
到
的距离最大值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835eb8216d9d7bf5c3290e47304f8bdd.png)
A.1 | B.![]() | C.![]() | D.2 |
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8 . 如图,点 是圆形舞台上的一点,舞台的圆心为
,在
点安装的一台某种型号的灯光装置,其照亮的区域如图中阴影所示,该装置可以绕着
点转动,转动过程中,边界的两条光线分别与圆交于
,
两点,并且夹角保持不变,该装置转动的过程中,以下结论正确的是( )
A.点 ![]() ![]() | B.弦 ![]() |
C.弦 ![]() ![]() | D.图中阴影部分的面积不变 |
您最近一年使用:0次
2024-03-25更新
|
108次组卷
|
2卷引用:北京市北京师范大学附属实验中学2023-2024学年九年级下学期开学考试数学试题
9 . 已知抛物线
经过点
.
(1)
和
的代数关系为________ ;
(2)若
,过点
作直线
轴,与
轴交于点
,
与抛物线交于另一点
,
,点
为直线
上方抛物线上一点,求点
到直线
距离的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11783577a1e29d8f67d4462252c4e770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c626cd8f49840ddf72cab2ec4c97c8c5.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c4afe5a7746350c965b080a47848f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/631aeeb0985f4a1ad439fdcc71960c5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f860799c66e6a48fe63fe1fa848bc83f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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真题
10 . 在平面直角坐标系中,给出如下定义:
为图形
上任意一点,如果点
到直线
的距离等于图形
上任意两点距离的最大值时,那么点
称为直线
的“伴随点”.
例如:如图1,已知点
,
,
在线段
上,则点
是直线
:
轴的“伴随点”.
(1)如图2,已知点
,
,
是线段
上一点,直线
过
,
两点,当点
是直线
的“伴随点”时,求点
的坐标;
(2)如图3,
轴上方有一等边三角形
,
轴,顶点A在
轴上且在
上方,
,点
是
上一点,且点
是直线
:
轴的“伴随点”.当点
到
轴的距离最小时,求等边三角形
的边长;
(3)如图4,以
,
,
为顶点的正方形
上始终存在点
,使得点
是直线
:
的“伴随点”.请直接写出
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
例如:如图1,已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/115a0c87ac14dbb770c95d74d6e26073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e5eea5f7f98ca8632358b7e49ceb25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2007972af3341f27fbc32ce62dfce5e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/30/235f620d-8fb6-4b10-a802-04b07d7ca365.png?resizew=550)
(1)如图2,已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ef03f452410ab19c6246567c427178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad434a7febc9d1491e73f51b86cd588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf77dad105b2686980eabe19b4e752a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)如图3,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05de5eef286a1b48012246c0cf88a1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cea7f618fa4919e4fcca69ed5958e99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(3)如图4,以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45f0ee968f9a247871a54e505fbd111b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9bd144e0e96e4236a14523e0729cacb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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