1 . 小亮同学喜欢研究数学问题.他在一本资料中看到一个新的数学概念“对角线互相垂直且相等的四边形叫做垂等四边形”,并对垂等四边形进行了研究.具体内容如下:
中,已知四边形
是垂等四边形,点A的坐标为
,点C的坐标为
,求点B的坐标;
(2)【规律初探】如图2,正方形
的边长为a,点E在边
上,点F在边
上,点G在边
上,点H在边
上,若四边形满足
,请直接写出四边形
面积S的取值范围;
(3)【综合探究】如图3,已知抛物线
与x轴交于M,N两点,点M在点N的左侧,P,Q两点在该抛物线上.若以M,N,P,Q为顶点的四边形是垂等四边形且
.设点P的横坐标为m,点Q的横坐标为n,且
,求m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea781875e43a5d70942f6e258054572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88a1f304d24f867811ff75447f50f15.png)
(2)【规律初探】如图2,正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9016de3d17a389fb5d0952f616c19e0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
(3)【综合探究】如图3,已知抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3236d825b994ee9c28e5d5479a57b8ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966a7257fd3af3a4049844773c611e26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7091d529281abff275ef19b9197445a7.png)
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