A专练7参考答案

专练7参考答案：

解：（1）假设四边形PQCM 是平行四边形，则PM ∥QC ，∴AP=AM ，即10﹣t=2t ，

解得t=

103

， ∴当t=103s 时，四边形PQCM 是平行四边形； （2）过P 作PE ⊥AC ，交AC 与E ，如图所示：

∵PQ ∥AC ，∴△PBQ ∽△ABC ，∴△PBQ 为等腰三角形，PQ=PB=t ，∴

BF BP BD BA =,即810

BF t =， 解得BF=45t ，∴FD=BD ﹣BF=8﹣45

t ，又∵MC=AC ﹣AM=10﹣2t ， ∴y= 21142()(102)88402255PQ MC FD t t t t t ??+=+--=-+ ??

?； （3）S △ABC =

111084022

AC BD =??=， 当y=916 S △ABC =94540162?=时，224584052t t -+=，解得12535,22t t ==（舍去）； （4）假设存在某一时刻t ，使得M 在线段PC 的垂直平分线上，则MP=MC ，过M 作MH ⊥AB ，交AB 与H ，∵∠A=∠A ，∠AHM=∠ADB=90°，∴△AHM ∽△ADB ，

∴HM AH AM BD AD AB

==，又6=， ∴28610HM AH t ==，∴86,55HM t AH t ==，即611101055HP t t t =--=-， 在直角三角形HMP 中，2222811371044100,555MP t t t t ????=+-=-+ ? ????

? 又∵MC 2=（10﹣2t ）2=100﹣40t+4t 2，∵MP 2=MC 2，即

223744100100404,5t t t t -+=-+ 解得：12017t =

，t 2=0，∴t=2017

s 时点M 在线段PC 的垂直平分线上．

2、解：（1）设抛物线的函数表达式为y=a （x –1）（x+3）

∵抛物线交y 轴于点E （0，–3），将该点坐标代入上式，得a=1

∴所求函数表达式为y=（x –1）（x+3），

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（三）

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