题目内容
已知点P在直线x+2y-1=0上,点Q在直线x+2y+3=0上,PQ中点为M(x0,y0),且y0>x0+2,则
的取值范围为________.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054113892476.png)
(-
,-
)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054113923339.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054113939306.png)
易知PQ的中点M应在直线x+2y+1=0上,即x0+2y0+1=0,又y0>x0+2,联立
,得交点坐标(-
,
),所以
=
,从几何意义上看,
表示点(x0,y0)与(0,0)连线的斜率.结合线性规划知识可知
的范围为(-
,-
).
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054113954897.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054113970355.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054114001324.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054113892476.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054114032562.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054113892476.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054113892476.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054113923339.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824054113939306.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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