如图1,平面直角坐标系中,直线
与x轴、y轴分别交于点A,B,直线y=-x+b经过点A,并与y轴交于点C.
![](https://img.xkw.com/dksih/QBM/2022/9/20/3070627243016192/3072684840460288/STEM/8d8c14a5f73c4bc9896aeab221c30479.png?resizew=359)
(1)求A,B两点的坐标及b的值;
(2)如图2,动点P从原点O出发,以每秒1个单位长度的速度沿x轴正方向运动.过点P作x轴的垂线,分别交直线AC,AB于点D,E.设点P运动的时间为t,点D的坐标为________,点E的坐标为________;(均用含t的式子表示)
(3)在(2)的条件下,当点P在线段OA上时,探究是否存在某一时刻,使DE=OB?若存在,求出此时△ADE的面积;若不存在说明理由.
(4)在(2)的条件下,点Q是线段OA上一点.当点P在射线OA上时,探究是否存在某一时刻使DE=
?若存在、求出此时t的值,并直接写出此时△DEQ为等腰三角形时点Q的坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24edd2a1d145627d07330524017daf5c.png)
![](https://img.xkw.com/dksih/QBM/2022/9/20/3070627243016192/3072684840460288/STEM/8d8c14a5f73c4bc9896aeab221c30479.png?resizew=359)
(1)求A,B两点的坐标及b的值;
(2)如图2,动点P从原点O出发,以每秒1个单位长度的速度沿x轴正方向运动.过点P作x轴的垂线,分别交直线AC,AB于点D,E.设点P运动的时间为t,点D的坐标为________,点E的坐标为________;(均用含t的式子表示)
(3)在(2)的条件下,当点P在线段OA上时,探究是否存在某一时刻,使DE=OB?若存在,求出此时△ADE的面积;若不存在说明理由.
(4)在(2)的条件下,点Q是线段OA上一点.当点P在射线OA上时,探究是否存在某一时刻使DE=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b64dc1ab9bf65cfdaac7633e9a7958ff.png)
21-22八年级上·广东深圳·期中 查看更多[4]
广东省深圳市南山区第二实验学校2021-2022学年八年级上学期期中考试数学试卷 (已下线)专题21 一次函数的应用之几何问题-【微专题】2022-2023学年八年级数学上册常考点微专题提分精练(北师大版)(已下线)专题1.31 三角形的证明(存在性问题)(培优篇)(专项练习)-2022-2023学年八年级数学下册基础知识专项讲练(北师大版)(已下线)难点特训(一)和三角形的证明有关的压轴大题-【微专题】2022-2023学年八年级数学下册常考点微专题提分精练(北师大版)
更新时间:2022-09-23 15:36:13
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相似题推荐
解答题-问答题
|
较难
(0.4)
【推荐1】在数轴上,点
、
表示的数分别为
、
,那么
、
两点之间的距离为
;反过来,式子
的几何意义是:数轴上表示数
的点和表示数
的点之间的距离.
已知点
在数轴上表示的数是
,点
表示的数为
,且满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/6/1b9a7ff2-2631-4812-9a5b-f5db0286015b.png?resizew=134)
(1)
______,
______,
______.(直接写出结果)
(2)如图1,点
是数轴上一点,点
到点
的距离是点
到点
的距离的3倍(即
),求点
在数轴上表示的数;
(3)如图2,点
,
分别从点
,
同时出发,分别以
,
的速度沿数轴负方向运动(
在
,
之间,
在
,
之间),运动时间为
秒,点
为
,
之间一点,且点
到
的距离是点
到
的距离的一半(即
),若
,
运动过程中
到
的距离(即
)总为一个固定的值,写出
与
的数量关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818c1773ef46692f12f1666e262bb2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5455c43cfafbffd00d1d5459069fc473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2795b34613d160327afdf70fb738c3c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/6/1b9a7ff2-2631-4812-9a5b-f5db0286015b.png?resizew=134)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
(2)如图1,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/5963abe8f421bd99a2aaa94831a951e9.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/6e453b8632aa8884baf3c804fc2d16ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)如图2,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f44c235d8b49207ad3f2d77dc5d6cf20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/814f55724f7ee57bd395eb3b95393c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88e177a27922d65bd6941a61166308b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f44c235d8b49207ad3f2d77dc5d6cf20.png)
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名校
解题方法
【推荐2】如图,在长方形
中,O为平面直角坐标系的原点,点A坐标为
,点C的坐标为
,且
满足
,点B在第一象限内,点P从原点出发,以每秒2个单位长度的速度沿着
的线路移动.
(1)点B的坐标为 ,当点P移动
秒时,点P的坐标为 ;
(2)在移动过程中,当点
到
轴的距离为
个单位长度时,求点
移动的时间;
(3)在移动过程中,当
的面积是
时,求点
移动的时间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d345e61f024bf07329cd27dc0bfadcf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64ba819698caf577d2d2d4c598c0f50a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ff2912fd8d93b6e692936d95b727c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92d51a7d3c2640b3d58b57810cb45fb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee55cc4cfffa7b34af0d8c53b7fcff6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/11/ea741020-f582-4444-9701-e08ebf106e3f.png?resizew=241)
(1)点B的坐标为 ,当点P移动
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d3bf727f6c78896544c7f6c8ff33ba.png)
(2)在移动过程中,当点
![](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/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)在移动过程中,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c8561afa0f1454ea382a625d000a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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解题方法
【推荐3】如图,在数轴.上有两个长方形
和
,这两个长方形的宽都是
个单位长度,长方形
的长
是
个单位长度,长方形
的长
是
个单位长度,点
在数轴上表示的数是
,且
两点之间的距离为
.
点
在数轴上表示的数是 ,点
在数轴上表示的数是
若线段
的中点为
,线段
上有一点
以每秒
个单位长度的速度向右匀速运动,
以每秒
个单位长度的速度向左运动,设运动的时间为
秒,问当
为多少时,原点
恰为线段
的三等分点?
若线段
的中点为
,线段
上有一点
,长方形
以每秒
个单位长度的速度向右匀速运动,长方形
保持不动,设运动时间为
秒,是否存在一个
的值,使以
三点为顶点的三角形是直角三角形?若存在,求
的值;不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589786dd7c3a2679c3230b671cd232d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/453ea8f3a2b85526b54bf453871c3820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa82a15632a545ce2cc6dc998899807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4bc45ba4c2ad98835bfdd40c2212ba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354ec8391bdd39377804ee4dab1d8f1c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/8/43cf86e1-1164-4e72-aad2-d9c3d9f05afd.png?resizew=254)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589786dd7c3a2679c3230b671cd232d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643efd9109bd9f23107e1b56da1425ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62295c36d2e2174908c2bec0eb5b30f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589786dd7c3a2679c3230b671cd232d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d97f4e3656f5b0ef2d30896db6daca41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db31b6ce9408706f77680ac8c75c2ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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解答题-问答题
|
较难
(0.4)
【推荐1】在平面直角坐标系
中,对于点
,我们称直线
为点P的关联直线,例如,点
的关联直线为
.
(1)已知点
.
①点A的关联直线为_________;
②若
与点A的关联直线相切,则
的半径为_________;
(2)已知点
,点
.点M为直线
上的动点.
①当
时,求点O到点M的关联直线的距离的最大值;
②以
为圆心,3为半径作
.在点M运动过程中,当点M的关联直线与
交于E,F两点时,
的最小值为4,请直接写出d的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee72603921c5dddcd01a62ed29ee0fb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89c1972246a0a3d1c987d25205dbdd99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497911bc462170183e81d95bd509b70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b5062be5cf27ae8089ad0c25d1b7c3.png)
(1)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6414faca343d19a90639b1d22b6f0b7.png)
①点A的关联直线为_________;
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3a83d984748f84098ccfaea864ea733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d8db024bd6f3c6c072a01c1652108cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c1344592c925b273f2cb9b9e47ebbb.png)
②以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29fe5fe4f22af30d6fec70689fedd02a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9347ab0d001ed7e8f51f9886ce88ac64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9347ab0d001ed7e8f51f9886ce88ac64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
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【推荐2】如图1,等腰直角三角形ABC中,∠ACB=90°,CB=CA,直线DE经过点C,过A作AD⊥DE于点D,过B作BE⊥DE于点E,则△BEC≌△CDA,我们称这种全等模型为“K型全等”.(不需要证明)
![](https://img.xkw.com/dksih/QBM/2020/8/1/2525532662587392/2525793444028416/STEM/6f1f38aa62de4a4dab7d6f5cc5db7d6b.png?resizew=517)
【模型应用】若一次函数y=kx+4(k≠0)的图象与x轴、y轴分别交于A、B两点.
(1)如图2,当k=﹣1时,若点B到经过原点的直线l的距离BE的长为3,求点A到直线l的距离AD的长;
(2)如图3,当k=﹣
时,点M在第一象限内,若△ABM是等腰直角三角形,求点M的坐标;
(3)当k的取值变化时,点A随之在x轴上运动,将线段BA绕点B逆时针旋转90°得到BQ,连接OQ,求OQ长的最小值.
![](https://img.xkw.com/dksih/QBM/2020/8/1/2525532662587392/2525793444028416/STEM/6f1f38aa62de4a4dab7d6f5cc5db7d6b.png?resizew=517)
【模型应用】若一次函数y=kx+4(k≠0)的图象与x轴、y轴分别交于A、B两点.
(1)如图2,当k=﹣1时,若点B到经过原点的直线l的距离BE的长为3,求点A到直线l的距离AD的长;
(2)如图3,当k=﹣
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d599cb4a589f90b0205f24c2e1fa021e.png)
(3)当k的取值变化时,点A随之在x轴上运动,将线段BA绕点B逆时针旋转90°得到BQ,连接OQ,求OQ长的最小值.
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【推荐3】在平面直角坐标系
中,对于直线
和点
,给出如下定义:
将点
向右
或向左
平移
个单位长度,再向上
或向下
平移
个单位长度,得到点
,将点
关于
轴对称点
称为点
关于直线
的“平移对称点”.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/30/b9b70634-3655-403b-afe8-5ef63de00bcb.png?resizew=141)
(1)如图,已知直线
为
.
①点
坐标为
,则点
关于直线
的“平移对称点”坐标为__________;
②在直线
上是否存在点
,使得点
关于直线
的“平移对称点”还在直线
上?若存在求出点
的坐标,若不存在请说明理由.
(2)已知直线
,若以点
为圆心,1为半径的圆上存在一点
,使得点
关于直线
的“平移对称点”在直线
上,直接写出
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6adf29eda2e0737ce81988fce9d751.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
将点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a083af79190de95296ab449077b4e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42b4ed2ac25cba0246a17b3fb527b73b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32380e5efccb4323c09c22f544ab85b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b151b08d8f44689da58500dfe9a90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3989d38e19836215cbc7c31868eee472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce22731a412796fe2925e01f765d5976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee6765a83140d745a6de4c85d9b6b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee6765a83140d745a6de4c85d9b6b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/30/b9b70634-3655-403b-afe8-5ef63de00bcb.png?resizew=141)
(1)如图,已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e15daf7b14dbff32c390f4984dcfb.png)
①点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f77ba8b3cb02c27e2a207a27a5f77701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
②在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35de69237f017e2fa34674d762683004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/862a5ffc6b7be4766713010c734f3720.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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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【推荐1】定义:把经过三角形的一个顶点并与其对边所在直线相切的圆叫做三角形的“切接圆”,根据上述定义解决下列问题:
在Rt△ABC中,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/11/d8113528-233b-48bf-9543-16cb7ecf5e8f.png?resizew=563)
(1)如图1,点D在AB边上,⊙D过点A且与BC相切于点E,则⊙D是Rt△ABC的一个“切接圆”,求该圆的的半径DE;
(2)过点A的Rt△ABC的“切接圆”中,是否存在半径的最小值,若存在请求出最小值,若不存在请说明理由;
(3)如图2,把Rt△ABC放在平面直角坐标系中,使点B与原点O重合,点C落在x轴正半轴上.求证:以抛物线
上任意一点为圆心都可以作过点A的Rt△ABC的“切接圆”.
在Rt△ABC中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a69550d878381f6e8fb436e88638f070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07140f277a35733d8c97577ccdd4e3ab.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/11/d8113528-233b-48bf-9543-16cb7ecf5e8f.png?resizew=563)
(1)如图1,点D在AB边上,⊙D过点A且与BC相切于点E,则⊙D是Rt△ABC的一个“切接圆”,求该圆的的半径DE;
(2)过点A的Rt△ABC的“切接圆”中,是否存在半径的最小值,若存在请求出最小值,若不存在请说明理由;
(3)如图2,把Rt△ABC放在平面直角坐标系中,使点B与原点O重合,点C落在x轴正半轴上.求证:以抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc165f444d87d722233791136c1f276f.png)
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【推荐2】如图1,在平面直角坐标系中,已知A(a,b),且a、b满足
,
(1)求A点的坐标及线段OA的长度;
(2)点P为x轴正半轴上一点,且△AOP是等腰三角形,求P点的坐标;
(3)如图2,若B(1,0),C(0,-3),试确定∠ACO+∠BCO的值是否发生变化,若不变,求其值;若变化,请求出变化范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc2b8276297c087b597461de61fccfb.png)
(1)求A点的坐标及线段OA的长度;
(2)点P为x轴正半轴上一点,且△AOP是等腰三角形,求P点的坐标;
(3)如图2,若B(1,0),C(0,-3),试确定∠ACO+∠BCO的值是否发生变化,若不变,求其值;若变化,请求出变化范围.
![](https://img.xkw.com/dksih/QBM/2019/5/24/2210462728060928/2217533798309888/STEM/0a7952d703bd4bc5a3561f58abae73bf.png?resizew=540)
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名校
【推荐1】已知平面直角坐标系中,直线
图象上有两点
和点
,与x轴交于点C,与y轴交于点D.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/28/32766a1b-50ba-4805-8a9a-bcd25ca3709a.png?resizew=205)
(1)求直线
的表达式;
(2)若在y轴上有一异于原点的点P,使
为等腰三角形,求点P的坐标;
(3)若将线段
沿直线
进行对折得到线段
,且点
始终在直线
上,当线段
与x轴有交点时,求n的取值的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8683204cc3cfd483d8bffffe8eba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e551782f2f549aa5f38868f10f00fe78.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/28/32766a1b-50ba-4805-8a9a-bcd25ca3709a.png?resizew=205)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若在y轴上有一异于原点的点P,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
(3)若将线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22bd12d5b2ee9c46f85a672d1261fbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
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【推荐2】如图,抛物线 y=﹣x2+bx+c 与 x 轴交于 A、B 两点,与 y 轴交于点 C ,点 A 的坐标为(-1,0),点 C 的坐标为(0,3),点D和点 C 关于抛物线的对称轴对称,直线 AD 与 y 轴交于点 E .
(1)求抛物线的解析式;
(2)如图,直线 AD 上方的抛物线上有一点 F,过点 F 作 FG⊥AD 于点 G,作 FH 平行于 x 轴交直线 AD 于点 H,求△FGH 周长的最大值.
(1)求抛物线的解析式;
(2)如图,直线 AD 上方的抛物线上有一点 F,过点 F 作 FG⊥AD 于点 G,作 FH 平行于 x 轴交直线 AD 于点 H,求△FGH 周长的最大值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/8/c9dd2df7-d725-4374-b1ee-d3df051fdfa4.png?resizew=393)
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