题目
题型:甘肃省中考真题难度:来源:
(1)在OC边上取一点D,将纸片沿AD翻折,使点O落在BC边上的点E处,求D,E两点的坐标;
(2)如图-2,若AE上有一动点P(不与A,E重合)自A点沿AE方向向E点匀速运动,运动的速度为每秒1个单位长度,设运动的时间为t秒(
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061256-47132.gif)
(3)在(2)的条件下,当t为何值时,以A,M,E为顶点的三角形为等腰三角形,并求出相应的时刻点M的坐标.
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061256-68695.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061256-49745.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061257-26309.gif)
∴在
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061257-88615.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061257-36899.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061257-36332.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061258-88637.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061258-83235.gif)
∴点E坐标为(2,4).
在
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061258-93106.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061259-27639.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061259-25180.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061259-40879.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061259-38608.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061300-37648.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061300-96283.gif)
(2)如图①
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061300-25066.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061301-55875.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061301-17957.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061301-71212.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061301-24737.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061302-94584.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061302-88357.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061302-65038.gif)
而显然四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061302-50371.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061303-11203.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061303-14450.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061303-95937.gif)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061303-35966.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061304-28169.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061304-97997.gif)
(3)(i)若以
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061304-73098.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061304-86864.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061305-47743.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061305-89408.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061305-75479.gif)
∴P为
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061305-74642.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061306-25741.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061306-64117.gif)
∴M为
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061306-57878.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061307-18847.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061307-81756.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061307-73058.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061308-49727.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061308-20365.gif)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061309-10707.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061309-46010.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061309-35431.gif)
此时点M坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061310-56582.gif)
(ii)若以AE为等腰三角形的腰,则
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061310-53967.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061310-96643.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061311-71319.gif)
过点M作
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061311-48552.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061311-85001.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061311-36357.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061312-88923.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061312-86204.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061312-40808.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061313-84861.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061313-22170.gif)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061313-58977.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061313-82858.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061314-85269.gif)
综合(i)(ii)可知,
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061314-45842.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061314-30602.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061315-74678.gif)
相应点M的坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061315-21322.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191101/20191101061315-95244.gif)
核心考点
试题【如图-1,OABC是一张放在平面直角坐标系中的矩形纸片,O为原点,点A在x轴的正半轴上,点C在y轴的正半轴上,OA=5,OC=4.(1)在OC边上取一点D,将纸】;主要考察你对勾股定理等知识点的理解。[详细]
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