![](http://thumb.1010pic.com/pic5/upload/201310/52856f0c07082.png)
解:(1)∵
![](http://thumb.1010pic.com/pic5/latex/398859.png)
.
∴a-2
![](http://thumb.1010pic.com/pic5/latex/21.png)
=0,b+4=0,
解得a=2
![](http://thumb.1010pic.com/pic5/latex/21.png)
,b=-4;
∴A(2
![](http://thumb.1010pic.com/pic5/latex/21.png)
,6),B(0.-4)
△AOB的面积为:
![](http://thumb.1010pic.com/pic5/latex/13.png)
×4×2
![](http://thumb.1010pic.com/pic5/latex/21.png)
=4
![](http://thumb.1010pic.com/pic5/latex/21.png)
;
(2)设直线AB的关系式为y=mx+n,
∵A(2
![](http://thumb.1010pic.com/pic5/latex/21.png)
,6),B(0.-4),
∴
![](http://thumb.1010pic.com/pic5/latex/398860.png)
,
解得
![](http://thumb.1010pic.com/pic5/latex/398861.png)
,
∴直线AB的关系式为y=
![](http://thumb.1010pic.com/pic5/latex/63299.png)
x-4,
当y=0时,x=
![](http://thumb.1010pic.com/pic5/latex/46499.png)
,
∴C(
![](http://thumb.1010pic.com/pic5/latex/46499.png)
,0),
设D(a,0),
∵S
△ACD=S
△BOC,
∴
![](http://thumb.1010pic.com/pic5/latex/13.png)
×6×(a-
![](http://thumb.1010pic.com/pic5/latex/46499.png)
)=4
![](http://thumb.1010pic.com/pic5/latex/21.png)
,
解得:a=
![](http://thumb.1010pic.com/pic5/latex/398862.png)
,
∴D点坐标(
![](http://thumb.1010pic.com/pic5/latex/398862.png)
,0);
(3)设x秒后OA′∥O′B,由题意得:
①当∠1=∠2时,(90-60)+4x=10x,
解得:x=5;
②当∠3=∠4时,180-(30+4x)=360-10x,
解得x=35,
答:在旋转过程中,经过10秒时间,OA′∥O′B.
分析:(1)根据非负数的性质可得a-2
![](http://thumb.1010pic.com/pic5/latex/21.png)
=0,b+4=0,再解方程即可;
(2)首先求出AB的直线解析式,再算出C点坐标,然后设D(a,0),根据S
△ACD=S
△BOC,可得
![](http://thumb.1010pic.com/pic5/latex/13.png)
×6×(a-
![](http://thumb.1010pic.com/pic5/latex/46499.png)
)=4
![](http://thumb.1010pic.com/pic5/latex/21.png)
,再解方程即可;
(3)此题要分两种情况进行讨论,①当∠1=∠2;②当∠3=∠4时分别计算.
点评:此题主要考查了平行线的判定与性质,一次函数解析式,以及非负数的性质,关键是考虑全面,不要漏解.