《九章算术》勾股章一五问“勾股容方”描述了关于图形之间关系的问题∶知道一个直角三角形较短直角边(“勾”)与较长直角边(“股”)的长度,那么,以该三角形的直角顶点为一个顶点、另外三个顶点分别在该三角形三边上的正方形的边长就可以求得.(我们不妨称这个正方形为该直角三角形的“勾容正方形”)
其文如下:
题:今有勾五步,股十二步,问勾中容方几何?
答:方三步,十七分步之九.
术:并勾、股为法,勾股相乘为实,实如法而一,得方一步.
“题”、“答”、“术”的意思大致如下∶
问题:一个直角三角形的两直角边的长分别为5和12,它的“勾容正方形”的边长是多少?
答案:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da6aeb767ea82b782addd1a74ce518a.png)
解法:
(1)问题探究
根据“勾股容方”中描述的直角三角形与其“勾容正方形”之间的关系,请提出一个数学命题,并证明;
(2)类比探究
“勾股容圆”:一个直角三角形的两直角边的长分别为5和12,它的内切圆的半径是多少?
(3)拓展运用
某市去年举办中小学校园文化展览,举办方在某广场搭建了一个展馆(平面示意图为正方形),并综合考虑参展主题、参展单位等因素将展馆划分为四个展区,规划方案如图所示,其中,
是
的中点,点
,
在
边上,
垂直平分
,垂足为
,
.
今年,为了让更多人参与,举办方拟在北湖公园的一块菱形场地上搭建展馆,该菱形场地面积为
,且两条对角线长度之和为
,考虑到展览安全、公园环境等各方面的因素,若举办方希望沿用去年展馆及展区的规划方案,则展馆的建设需满足以下要求:①展馆平面示意图中的A,B,C,D四个点分别落在菱形场地的四条边上;②展馆主入口
的宽度为
,去年的规划方案是否可行?请说明理由.
其文如下:
题:今有勾五步,股十二步,问勾中容方几何?
答:方三步,十七分步之九.
术:并勾、股为法,勾股相乘为实,实如法而一,得方一步.
“题”、“答”、“术”的意思大致如下∶
问题:一个直角三角形的两直角边的长分别为5和12,它的“勾容正方形”的边长是多少?
答案:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da6aeb767ea82b782addd1a74ce518a.png)
解法:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d55e5ab49750c88c2cc1adbe3784c5ca.png)
(1)问题探究
根据“勾股容方”中描述的直角三角形与其“勾容正方形”之间的关系,请提出一个数学命题,并证明;
(2)类比探究
“勾股容圆”:一个直角三角形的两直角边的长分别为5和12,它的内切圆的半径是多少?
(3)拓展运用
某市去年举办中小学校园文化展览,举办方在某广场搭建了一个展馆(平面示意图为正方形),并综合考虑参展主题、参展单位等因素将展馆划分为四个展区,规划方案如图所示,其中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b95463a97c60db3250cb641bf6523d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9954fb448161566ce61787f143ff0cd4.png)
今年,为了让更多人参与,举办方拟在北湖公园的一块菱形场地上搭建展馆,该菱形场地面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb81e2e2edd68c29eaca8841717566d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05ba29eb90358e2211e1f7ba6423fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e978c77cb0d7eff794447241e9829867.png)
更新时间:2024-06-04 20:47:26
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相似题推荐
解答题-问答题
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解题方法
【推荐1】综合与实践
实践操作:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/b611be03-0992-4f5c-afc2-6a0ecdbe63cf.png?resizew=403)
①如图1,
是等边三角形,D为BC边上一个动点,将
绕点A逆时针旋转
得到
,连接CE.
②如图2,在
中,
于点D,将
绕点A逆时针旋转
得到
,延长FE与BC交于点G.
③如图3,将图2中得到
沿AE再一次折叠得到
,连接MB.
问题解决:
(1)小明在探索图1时发现四边形ABCE是菱形.小明是这样想的:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/7fe6a39f-651a-4ec1-be22-e5af6a03708b.png?resizew=727)
请根据小明的探索直接写出图1中线段CD,CF,AC之间的数量关系为 :
(2)猜想图2中四边形ADGF的形状,并说明理由;
问题再探:
(3)在图3中,若AD=6,BD=2,则MB的长为 .
实践操作:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/b611be03-0992-4f5c-afc2-6a0ecdbe63cf.png?resizew=403)
①如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f8f01137e92c0f2e63467036ae9cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f201a40fedca4ad14db193f4db2127e.png)
②如图2,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5e1441a49e782ff0ef46e776cde06a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f201a40fedca4ad14db193f4db2127e.png)
③如图3,将图2中得到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f201a40fedca4ad14db193f4db2127e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6a158e8a768a5fec8c934ce75038df.png)
问题解决:
(1)小明在探索图1时发现四边形ABCE是菱形.小明是这样想的:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/7fe6a39f-651a-4ec1-be22-e5af6a03708b.png?resizew=727)
请根据小明的探索直接写出图1中线段CD,CF,AC之间的数量关系为 :
(2)猜想图2中四边形ADGF的形状,并说明理由;
问题再探:
(3)在图3中,若AD=6,BD=2,则MB的长为 .
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【推荐2】在
中,
,
,点
为
边上一动点,且
,
交
边于点
.探究:如图1,若
.
时,求
的长;
(2)当
为等腰三角形时,求
的长;
(3)延伸:如图2,若
,
为
上一点,且
.小东经过研究发现:“当点
在
边上运动时,
的长度不变,是个定值.”你认为小东的结论是否正确?如果正确,请求出这个定值;如果不正确,说明理由;
(4)若
,直接写出
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05d35d8d8bb0dc17f2f86fe5b230a2b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c14a66ed4bd66df65bc42c4ac1ed15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983d4402fddd33c1cc85ebc1711d2c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.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/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a6ac027fb5985958afa2fe35d3d4e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df7626240940eb340420a605e95aeee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
(3)延伸:如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc60f2fd9c91293a743111539202a169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6618b4d41917e695da2356c016242ba4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee7cc5c75476896a599093f5ac10b97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e5d4f93699f8dcffb0e7840ca5597e.png)
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【推荐1】【问题提出】
(1)如图1,在
中,
,
,
为
边上的高,则
的长为______.
(2)如图2,在四边形
中,
,且
,E,F分别是
的中点,连接
与
相交于点M,
与
相交于点O,若
,求
的长.
【问题解决】
(3)如图3,四边形
是园林局欲修建的一块菱形园地的大致示意图,沿对角线
各修一条人行走道,
.E是
上的一点,点F,G在
上,
,
.根据规划要求,建造一个四边形OEFG的特殊花卉种植区,求该种植区四边形OEFG的最大面积.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/4/32e0934c-4f72-4ab8-ac4d-b59702261514.png?resizew=538)
(1)如图1,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04952752bd4ae5692e2b3199cb79d99f.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/03902478df1a55bc99703210bccab910.png)
(2)如图2,在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12143a06ed24558d8cc7ad39961d3e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667f534c3893e5dcfe16be356202971a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9bd5a32b84e449bf7900b433321e5f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/565a57772ad9357e1cac02a8fa40ab81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
【问题解决】
(3)如图3,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5168335544ab74e8107b46ab5b7ec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0c20c10a0bcc450a4c3ea5396db0f91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab00e0cff0876c4183a47f1272cf9928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65e4cebc6796d315aa40a9a535f92cd.png)
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【推荐2】如图,在平面直角坐标系
中,菱形
,
,
,
过点
作
轴交
于点
,直线
分别交
轴和
轴于点
和点
,动点
从点
出发以每秒2个单位长度的速度沿
向终点
运动,设运动时间为
秒.
(1)求直线
的解析式;
(2)求当
为何值时,
;
(3)点
在运动的过程中,在坐标平面内是否存在一点
,使得以
,
,
,
为顶点的四边形是矩形.若存在,直接写出点
的坐标,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e3fa43e765646223675ef9bbd6d2f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79684a6e92297749c005e2b23cac9710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9adc47184160600048adb7b24c651269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c9f25703e265026af2d481e64414d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2634263d383b0487281fdcf6fe3cc625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c57b07f75e97d9f84718bd495ebcf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/11/51a4b389-612a-4252-8f68-907bfdf83296.png?resizew=199)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)求当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5aee44ee14c7a1beb212553650c990.png)
(3)点
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/acc290b44635265137fdf13146b6a6d9.png)
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【推荐1】(1)问题呈现:如图1,
和
都是直角三角形,
,且
.连接
,
,求
的值.
(2)类比探究:如图2,
是等腰直角三角形,
,将
绕点
逆时针旋转
得到
,连接
,
,延长
交
于点
,设
,求
的长;
(3)拓展提升:如图3,在等边
中,
,
是
边上的中线,点
从点
移动到点
,连接
,以
为边长,在
的上方作等边
,求点
经过的路径长.
![](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/21c2425db34d83dbe44f3ee3d2c5439b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822765a2749e69de3f630c456c554cc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9af91834644b94e1b023b33e15a0644.png)
(2)类比探究:如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(3)拓展提升:如图3,在等边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e856c15c61d7cb6ebd8daef542a4e7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
【推荐2】在平面直角坐标系中,点
为原点,点
的坐标为
.如图1,正方形
的顶点
在
轴的负半轴上,点
在第二象限.现将正方形
绕点
顺时针旋转角
得到正方形
.
(1)如图2,若
,
,求直线
的函数表达式.
(2)若
为锐角
,当
取得最小值时,求正方形
的面积.
(3)当正方形
的顶点
落在
轴上时,直线
与直线
相交于点
,
的其中两边之比能否为
?若能,求点
的坐标;若不能,试说明理由.
![](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/7f79821f22f666a97f26d3350512f5da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab158dd9e96abcae0f115f54fa66c5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab158dd9e96abcae0f115f54fa66c5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b670c6d27ce68f17ac12c4efa1933db1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/9/e0e7933a-2628-41eb-bf67-07860eeb7b64.png?resizew=418)
(1)如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c96cb3ac8290e09c55d4eb336a8608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/539017d54be655fef3e26d2292a58e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18fafc016dedb418df05cdbb12305f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b670c6d27ce68f17ac12c4efa1933db1.png)
(3)当正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b670c6d27ce68f17ac12c4efa1933db1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a70b91e48c6c0435789cc656a19465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d76e86c1dcc191aa8d51b3a528a454d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
解答题-问答题
|
困难
(0.15)
【推荐1】如图,在平面直角坐标系xOy中,点O为坐标原点,抛物线
与x轴交于A、B两点(点A在点B的左侧),与y轴交于点C,点B的坐标为(3,0),直线
经过B、C两点.
(1)求抛物线的解析式;
(2)点P是x轴下方抛物线上一点,连接AC,过点P作PQ∥AC交BC于点Q,过点Q作x轴的平行线,过点P作y轴的平行线,两条直线相交于点K,PK交BC于点H,设QK的长为t,PH的长为d,求d与t之间的函数关系式;(不要求写出自变量t的取值范围)
(3)在(2)的条件下,PK交x轴于点R,过点R作RT⊥PQ,垂足为T,当PK=
PT时,将线段QT绕点Q逆时针旋转90
得到线段QL,M是线段PQ上一动点,过点M作直线AC的垂线,垂足为N,连接ON、ML,当ML∥ON时,求N点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd1079ddc80f8b73effaed2efc641175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8188f3111d144ac9b7c30529c48401.png)
(1)求抛物线的解析式;
(2)点P是x轴下方抛物线上一点,连接AC,过点P作PQ∥AC交BC于点Q,过点Q作x轴的平行线,过点P作y轴的平行线,两条直线相交于点K,PK交BC于点H,设QK的长为t,PH的长为d,求d与t之间的函数关系式;(不要求写出自变量t的取值范围)
(3)在(2)的条件下,PK交x轴于点R,过点R作RT⊥PQ,垂足为T,当PK=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e84accbdfc051019a7c6c1df40b871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83873a9d782f2588c5eedbfe73f9bc2f.png)
![](https://img.xkw.com/dksih/QBM/2018/4/3/1916155567259648/1920231368146944/STEM/057ff365464b42fdb6abf3b5229ef1e9.png?resizew=511)
您最近一年使用:0次
解答题-问答题
|
困难
(0.15)
【推荐2】在平面直角坐标系中,已知
,点C在第一象限内,点D与点A关于y轴对称,且四边形
是平行四边形.
(2)在图1中,用尺规作图确定C点位置(不写做法,保留作图痕迹)
(3)如图2,现有半径为1的
,若其圆心P从点A出发,沿着
以每秒4个单位长的速度匀速移动,同时
的半径以每秒0.5个单位长度的速度增加,运动到点C时运动停止,当运动时间为t秒时:
①t为何值,
与y轴相切?
②在整个运动过程中,
与y轴有公共点的时间共有 秒.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ba5d8633843a107219de697a6bb81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)在图1中,用尺规作图确定C点位置(不写做法,保留作图痕迹)
(3)如图2,现有半径为1的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4592635ab30a7f307bc02b67163ddbab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
①t为何值,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
②在整个运动过程中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
您最近一年使用:0次