解:(1)假设四边形PQCM是平行四边形,则PM∥ QC,∴AP=AM ∴ ,解得![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103093839-69965.gif) 答:当 s时,四边形PQCM是平行四边形。 (2)过P作PE⊥AC,交AC于E。
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103093840-50735.jpg) ∵PQ∥AC ∴△PBQ∽△ABC,∴△PBQ是等腰三角形,PQ=PB= , ∴ ,即 ,解得 , ∴![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103093840-70468.gif) 又∵ , ∴![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103093841-84983.gif) 答:y与t之间的函数关系式是![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103093842-30936.gif) (3)![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103093842-18934.gif) 当 时,
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103093842-45871.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103093842-72020.gif) 解得![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103093842-85749.gif) , (舍去) 答:当 时,S四边形PQCM=S△ABC (4)假设存在某一时刻t,使点M在线段PC的垂直平分线上,则MP=MC, 过M作MH⊥AB,交AB于H,由△AHM∽△ADB
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103093843-35524.jpg) ∴ ,又![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103093844-77158.gif) ∴ , ∴![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103093845-48935.gif) 即![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103093845-22511.gif) 在Rt△HMP中,
![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103093845-81390.gif) 又∵![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103093845-80373.gif) 由![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103093845-44201.gif) ∴![](http://img.shitiku.com.cn/uploads/allimg/20191103/20191103093846-73309.gif) 解得: (舍去) 答:当 s时,点M在线段PC的垂直平分线上。 |