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【简答题】
(2013年浙江义乌10分)合作学习小组在探究旋转、平移变换.如图△ABC,△DEF均为等腰直角三角形,各顶点坐标分别为A(1,1),B(2,2),C(2,1),D( ,0),E( , 0),F( , ). (1)他们将△ABC绕C点按顺时针方向旋转45 0 得到△A 1 B 1 C.请你写出点A 1 ,B 1 的坐标,并判断A 1 C和DF的位置关系; (2)他们将△ABC绕原点按顺时针方向旋转45 0 ,发现旋转后的三角形恰好有两个顶点落在抛物线 上.请你求出符合条件的抛物线解析式; (3)他们继续探究,发现将△ABC绕某个点旋转45,若旋转后的三角形恰好有两个顶点落在抛物线 上,则可求出旋转后三角形的直角顶点P的坐标.请你直接写出点P的所有坐标.
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