题目
题型:解答题难度:一般来源:不详
点D为线段BC的中点,动点P从点O出发,以每秒1个单位的速度,沿折线OABD的路线移动,移动的时间为
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212443-96273.png)
(1)求直线BC的解析式;
(2)若动点P在线段OA上移动,当
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212443-96273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212444-31511.png)
(3)动点P从点O出发,沿折线OABD的路线移动过程中,设△OPD的面积为S,请直接写出S与
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212443-96273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212443-96273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212445-33906.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212445-61473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212445-47627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212445-47809.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212446-36328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212446-83277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212445-61473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212446-36160.png)
(2)如图,取OA的中点E,连接DE.
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212446-25179.png)
∵D、E分别为梯形OCBA两腰的中点
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212446-90443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212447-30260.png)
∴DE∥OC∥AB,
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212447-83233.png)
∵OC⊥OA
则
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212447-68313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212447-97309.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212448-61483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212448-82041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212448-13106.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212448-72869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212448-60186.png)
如图,
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212449-67644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212449-49508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212449-53652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212449-88271.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212450-44269.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212450-75909.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212450-70524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212450-73932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212451-37545.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212451-92382.png)
解析
(2)可根据四边形OPDC的面积是梯形COAB面积的
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212451-77474.png)
(3)要根据P的位置在不同边的具体情况利用相关的知识写出函数关系式及取值范围.
核心考点
试题【已知,如图,在直角梯形COAB中,OC∥AB,以O为原点建立平面直角坐标系,A、B、C三点的坐标分别为A(8,0),B(8,10),C(0,4),点D为线段BC】;主要考察你对计算器计算等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212439-71794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212425-17486.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212425-39145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212425-85492.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212425-54524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212425-23315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212423-55143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212423-31993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212423-49342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212423-31993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212423-55143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212423-93455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212417-41416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212417-21538.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212417-67715.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212418-76077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212418-69732.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212418-81512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212414-32767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212414-66790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212414-57389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212414-63886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190816/20190816212415-19007.png)
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