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
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名校
5 . (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)
您最近一年使用:0次
真题
6 . 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)
您最近一年使用:0次
7 . 如图,抛物线
与
轴相交于点
、
,与
轴相交于点
,抛物线对称轴与
轴相交于点
,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/5fcc361c-9487-4cd6-9a07-b79916943a93.png?resizew=143)
(1)求
的面积;
(2)若
是
轴上方的抛物线上的一个动点,求点
到直线
的距离的最大值;
(3)若点
在抛物线上运动(点
异于点),当
时,求直线
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2360befae52b72f55db50833fc7103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/5fcc361c-9487-4cd6-9a07-b79916943a93.png?resizew=143)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(3)若点
![](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/75d78e9bf9bb5aae33fb1dfde98f2ba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
您最近一年使用:0次
8 . 如图,
和
中,
,
,
,边
与边
交于点
(不与点
,
重合),点
,
在
异侧,
为
与
的角平分线的交点.
![](https://img.xkw.com/dksih/QBM/2022/1/20/2898449736187904/2921335431675904/STEM/9cc96e3d-e6fa-4cb2-8a23-ac054e782c2d.png?resizew=470)
(1)求证:
;
(2)设
,请用含
的式子表示
,并求
的最大值;
(3)当
时,
的取值范围为
,求出
,
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4362edfc026266c5d29b3f90df374e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5adc18ca424552b35ab939e9d57943e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357d001bbcaffdd67399472fd3120ee8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32986401a4d24904d5e446fa9210ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172766b458ea1e95ab1f5cd70bab7463.png)
![](https://img.xkw.com/dksih/QBM/2022/1/20/2898449736187904/2921335431675904/STEM/9cc96e3d-e6fa-4cb2-8a23-ac054e782c2d.png?resizew=470)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5cc2450dc300ce26b513c2abae28cab.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8711eddf26d11fc974dfb6da4b640918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce9e3c97a03095a8372d09f2ff6727cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68a0037b50b07562417d47d1026723b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
20-21八年级上·广东深圳·期中
名校
9 . 对于两个已知图形G1、G2,在G1上任取一点P,在G2上任取一点Q,当线段PQ的长度最小时,我们称这个最小的长度为图形G1、G2的“密距”;当线段PQ的长度最大值时,我们称这个最大的长度为图形G1、G2的“疏距”.
请你在学习、理解上述定义的基础上,解决下面的问题;
在平面直角坐标系xOy中,点A的坐标为(-3,4),点B的坐标为(3,4),矩形ABCD的对称中心为点O.
(1)线段AD和BC的“密距”是________,“疏距”是________;
(2)设直线
与x轴、y轴分别交于点E、F,若线段EF与矩形ABCD的“密距”是1,求它们的“疏距”;
(3)平面直角坐标系xOy中有一个四边形KLMN,将矩形ABCD绕点O旋转一周,在旋转过程中,它与四边形KLMN的“疏距”的最大值为7,
①旋转过程中,它与四边形KLMN的“密距”的取值范围是________;
②求四边形KLMN的面积的最大值.
请你在学习、理解上述定义的基础上,解决下面的问题;
在平面直角坐标系xOy中,点A的坐标为(-3,4),点B的坐标为(3,4),矩形ABCD的对称中心为点O.
(1)线段AD和BC的“密距”是________,“疏距”是________;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/203fb787f665de741882bdc9adbfd168.png)
(3)平面直角坐标系xOy中有一个四边形KLMN,将矩形ABCD绕点O旋转一周,在旋转过程中,它与四边形KLMN的“疏距”的最大值为7,
①旋转过程中,它与四边形KLMN的“密距”的取值范围是________;
②求四边形KLMN的面积的最大值.
![](https://img.xkw.com/dksih/QBM/2021/12/10/2869694731763712/2874205893263360/STEM/6c7db3be-98ba-4a63-8be2-8f50cc69caf2.png?resizew=547)
您最近一年使用:0次
名校
解题方法
10 . 提出问题:已知平面直角坐标系内,任意一点A,到另外一个点B之间的距离是度多少?
问题解决:
(1)遇到这种问题,我们可以先从特例入手,最后推理得出结论
探究一:点A(1,﹣1)到B(﹣1,﹣1)的距离d1= ,
探究二:点A(2,﹣2)到B(﹣1,﹣1)的距离d1= ,
一般规律:
如图1,在平面直角坐标系xoy内已知A(x1,y1)、B(x2,y2),我们可以表示连接AB,在构造直角三角形,使两条边交于M,且∠M=90°,此时AM= ,BM= ,AB= .
![](https://img.xkw.com/dksih/QBM/2021/11/3/2843122612125696/2844060521144320/STEM/a95be408-e347-46f1-8432-5706e3da3b0c.png?resizew=468)
材料补充:已知点P(x0,y0)到直线y=kx+b的距离d2可用公式d2=
计算.
问题解决:
(2)已知互相平行的直线y=x﹣2与y=x+b之间的距离是3
,试求b的值.
拓展延伸:
拓展一:已知点M(﹣1,3)与直线y=2x上一点N的距离是3,则△OMN的面积是 .
拓展二:如图2,已知直线y=
分别交x,y轴于A,B两点,⊙C是以C(2,2)为圆心,2为半径的圆,P为⊙C上的动点,试求△PAB面积的最大值.
问题解决:
(1)遇到这种问题,我们可以先从特例入手,最后推理得出结论
探究一:点A(1,﹣1)到B(﹣1,﹣1)的距离d1= ,
探究二:点A(2,﹣2)到B(﹣1,﹣1)的距离d1= ,
一般规律:
如图1,在平面直角坐标系xoy内已知A(x1,y1)、B(x2,y2),我们可以表示连接AB,在构造直角三角形,使两条边交于M,且∠M=90°,此时AM= ,BM= ,AB= .
![](https://img.xkw.com/dksih/QBM/2021/11/3/2843122612125696/2844060521144320/STEM/a95be408-e347-46f1-8432-5706e3da3b0c.png?resizew=468)
材料补充:已知点P(x0,y0)到直线y=kx+b的距离d2可用公式d2=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b86cd15f64e28a2d440712312e3158a.png)
问题解决:
(2)已知互相平行的直线y=x﹣2与y=x+b之间的距离是3
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
拓展延伸:
拓展一:已知点M(﹣1,3)与直线y=2x上一点N的距离是3,则△OMN的面积是 .
拓展二:如图2,已知直线y=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1766790d350df38aa14879e09da42a.png)
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2021-11-04更新
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4卷引用:山东省青岛市市南区2021-2022学年八年级上学期期中数学试题
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