题目内容
(本小题满分12分)
已知
的三个顶点
.
(Ⅰ)求
边所在直线方程;
(Ⅱ)
边上中线
的方程为
,且
,求
的值.
已知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003650674544.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240036506901059.png)
(Ⅰ)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003650799398.png)
(Ⅱ)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003650799398.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003650846387.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003650862683.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003650877601.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003650893435.png)
(Ⅰ)
(Ⅱ)
或![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003650955647.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003650908622.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003650924636.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003650955647.png)
试题分析:(Ⅰ)根据两点间的斜率公式可知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003650971792.png)
根据直线的点斜式方程有
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003650971795.png)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003650799398.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003650908622.png)
(Ⅱ)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240036510331158.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240036510491060.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003651064554.png)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003651080974.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003651111579.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003651127600.png)
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240036511421067.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240036511741070.png)
解得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003650924636.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824003650955647.png)
点评:求解直线方程时,要灵活运用直线方程的五种形式,更要注意各自的适用范围和限制条件;另外,点到直线的距离公式在解题时经常用到,要灵活应用.
![](http://thumb.zyjl.cn/images/loading.gif)
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