如图,在平面直角坐标系中,点A,B的坐标分别为
和
,动点
从点
出发在线段
上以每秒两个单位长度的速度向点O运动,动直线
从
轴开始以每秒1个单位长度的速度向上平行移动(即
轴),分别与
轴和线段
交于点
,
,连接
,
.设动点
和动直线
同时出发,运动时间为
秒(动点
和动直线
有一个停止运动,则另一个也停止运动).
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/21/833688d0-950b-4b72-b6d1-48b0c8a0711e.png?resizew=201)
(1)当
时,
的面积为________;
(2)求在动点
和动直线
运动的过程中,使
的面积为24时的
值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c6f8e173e33cb03b862f4f763147a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e6b41aeb74ed128607a74ed1a61db21.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/e2c3d2cba96f6f03520c0b3f6e4da03e.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/0450e9660d59d577a0cec74b72950f81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f541f7ae7c39082d202efd28805c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c2293f93791a597bf0162411f3395f.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/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/21/833688d0-950b-4b72-b6d1-48b0c8a0711e.png?resizew=201)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822921b3e0b6db0ce9c8b4a56043e9e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b51d3992644d37dc71c9b5a97d515c.png)
(2)求在动点
![](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/91b51d3992644d37dc71c9b5a97d515c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
更新时间:2024-01-21 08:42:27
|
相似题推荐
解答题-计算题
|
适中
(0.65)
名校
【推荐1】当解某些计算较复杂的一元二次方程时,可考虑用“缩根法”简化运算.“缩根法”是指将一元二次方程先转化成系数比原方程简单的新一元二次方程,然后解新一元二次方程,并将新方程的两根同时缩小,从而得到原方程的两个根.
已知:关于
的一元二次方程
的两个根分别为
,
,求关于
的一元二次方程
的两根.
解:因为
,
所以
.
令
,得新方程
.
因为新方程的解为
,
,所以
,
,所以原方程的两个根分别为
,
.
这种解一元二次方程的方法叫做“缩根法”.
举例:用缩根法解方程
.
解:因为
,
,所以
,令
,得新方程
.
解新方程,得
,
,所以
,
,
所以原方程的两个根分别为
,
.
请利用上面材料中的缩根法解下列方程:
(1)
;
(2)
.
已知:关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/807d62d0b5623b3bd3cb285560bf8436.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c260fdd494924bad62ce5644097428e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/766ef277ff879c9129b0c55dce9b248f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75964e6c72c9a1c930613222a6e854ae.png)
解:因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75964e6c72c9a1c930613222a6e854ae.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7943176ce206fab53ff1df5aa5279f50.png)
令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640ce865a99b1d34ec05eb826fbb02f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abfce8b3309453460da0e492b3e0392d.png)
因为新方程的解为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be94f17cf66472e510a6091051e7b3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a14839f0d1c60eb02286b88517a3a229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5923a1db98b155188696961e078a02c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d507244347198de6c3e736b210d45e40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0b387fd4cdad224eee340764c964cd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de4ef79325ec3a634939c29f59d673a.png)
这种解一元二次方程的方法叫做“缩根法”.
举例:用缩根法解方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce6bde2f3308e5182b8516e2f62aced.png)
解:因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d2e0709918109d428624c80ab545b12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de653a545c4cf2c2b8a4c5fbec8198cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a8de232ba167b271d1eda5e631fbf41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b4a4cdadaa4d08bbedbc0eec1475578.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f413192ed26f2d90d7995574abce6698.png)
解新方程,得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7b9fe3863cba4804a31b6b831485bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec787c243c5cd568f4d0a4fd1ff057f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7594e3b868687e2042b8e94ee65c26e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/049827d1ecd52eafcc5448d94db31937.png)
所以原方程的两个根分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfacad9f14139ff606705a83c138d5ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79a7941c74347f59b04fac7509868a7.png)
请利用上面材料中的缩根法解下列方程:
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8cf3e5c644a9e1a16422742e5c07267.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a9ca96281e386bf74dfcf8882fae3d2.png)
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解答题-作图题
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适中
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【推荐1】如图,已知A(﹣4,﹣1),B(﹣5,﹣4),C(﹣1,﹣3),△ABC经过平移得到的
,△ABC中任意一点P(x1,y1)平移后的对应点为
(x1+6,y1+4).
![](https://img.xkw.com/dksih/QBM/2022/4/26/2966321807867904/2970778995867648/STEM/8af68fe5-47de-4ae3-b9dd-98aa14c380d3.png?resizew=267)
(1)写出点
、
、
的坐标.
(2)请在图中作出
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ee6e1d480ece7117e1f87ebf4bbeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee6765a83140d745a6de4c85d9b6b50.png)
![](https://img.xkw.com/dksih/QBM/2022/4/26/2966321807867904/2970778995867648/STEM/8af68fe5-47de-4ae3-b9dd-98aa14c380d3.png?resizew=267)
(1)写出点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
(2)请在图中作出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ee6e1d480ece7117e1f87ebf4bbeea.png)
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解答题-问答题
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适中
(0.65)
【推荐2】已知点A(4m﹣6,0),B(0,m+3)分别为两坐标轴正半轴上一点,OA=OB.
(1)求m的值及点A、点B的坐标;
(2)若点D为线段OA上一点(不与O,A重合).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/83a4265e-9264-46aa-b34c-169d4ed08098.png?resizew=172)
①如图1,将线段BO沿直线BD翻折,使点O落在AB边上的点E处,点P是直线BD上一动点,求△PEA的周长的最小值;
②如图2,点F为AB的中点,点C在y轴负半轴上,若AD+OC=CD,则∠CFD的大小是否发生改变,若不变,请求出∠CFD度数;若变化,请说明理由.
(1)求m的值及点A、点B的坐标;
(2)若点D为线段OA上一点(不与O,A重合).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/406cf87b-fb9c-479d-87ab-9e9e88f9087e.png?resizew=177)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/83a4265e-9264-46aa-b34c-169d4ed08098.png?resizew=172)
①如图1,将线段BO沿直线BD翻折,使点O落在AB边上的点E处,点P是直线BD上一动点,求△PEA的周长的最小值;
②如图2,点F为AB的中点,点C在y轴负半轴上,若AD+OC=CD,则∠CFD的大小是否发生改变,若不变,请求出∠CFD度数;若变化,请说明理由.
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解答题-问答题
|
适中
(0.65)
【推荐1】如图,矩形
和矩形
,要判定他们是否相似,小明有以下2种方法.
①如图1,将
放在
上,连接
并延长与
交于点
.若点
在同一直线上,则矩形
和矩形
相似;
②如图2,连接
和
,若
,则矩形
和矩形
相似.
上述说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/30/2997ce69-8ee5-4ef5-851e-fb7c82933735.png?resizew=476)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
①如图1,将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e4fa04825ac7d071968056322d88be.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/cd16fbdf9ce8c3bce5a23436d88d29c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
②如图2,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa3205b1df826d63914dcb55bb3ab43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
上述说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/30/2997ce69-8ee5-4ef5-851e-fb7c82933735.png?resizew=476)
A.①②都对 | B.①②都错 | C.①对②错 | D.①错②对 |
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解答题-证明题
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适中
(0.65)
名校
【推荐2】如图,在四边形
中
,且
,垂足为
,
延长线交
于
,交
的延长线于
.
(1)求证:A,
,
,
四点共圆;
(2)求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/728a6fe72c0a2df665c778676ffd90b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bad3d9422cf9c0b078900b3c507e87c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/24/4c9020f0-c06b-49f3-a3d7-b3aa64822244.png?resizew=213)
(1)求证:A,
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3cfcc8a1cc42fdadd5053172bb7d0c9.png)
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