在平面直角坐标系中，O为原点，点A（-2，0），点B（0，2），点E，点F分别为OA，OB的中点．若正方形OEDF绕 在平面直角坐标系中xOy中，点A与原点O重合，点B（4，0）...
\u5728\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\uff0cO\u4e3a\u539f\u70b9\uff0c\u70b9A\uff08-2,0 \uff09\uff0c\u70b9B\uff080,2\uff09\uff0c\u70b9E,F\u5206\u522b\u4e3aOA,OB\u7684\u4e2d\u70b9\u3010\u9898\u76ee\u3011
\u5728\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\uff0cO\u4e3a\u539f\u70b9\uff0c\u70b9A\uff08-2\uff0c0\uff09\uff0c\u70b9B\uff080\uff0c2\uff09\uff0c\u70b9E\uff0c\u70b9F\u5206\u522b\u4e3aOA\uff0cOB\u7684\u4e2d\u70b9\uff0e\u82e5\u6b63\u65b9\u5f62OEDF\u7ed5\u70b9O\u987a\u65f6\u9488\u65cb\u8f6c\uff0c\u5f97\u6b63\u65b9\u5f62OE\u2032D\u2032F\u2032\uff0c\u8bb0\u65cb\u8f6c\u89d2\u4e3a\u03b1\uff0e
\uff08\u2160\uff09\u5982\u56fe\u2460\uff0c\u5f53\u03b1=90\u00b0\u65f6\uff0c\u6c42AE\u2032\uff0cBF\u2032\u7684\u957f\uff1b\uff08\u2161\uff09\u5982\u56fe\u2461\uff0c\u5f53\u03b1=135\u00b0\u65f6\uff0c\u6c42\u8bc1AE\u2032=BF\u2032\uff0c\u4e14AE\u2032\u22a5BF\u2032\uff1b\uff08\u2162\uff09\u82e5\u76f4\u7ebfAE\u2032\u4e0e\u76f4\u7ebfBF\u2032\u76f8\u4ea4\u4e8e\u70b9P\uff0c\u6c42\u70b9P\u7684\u7eb5\u5750\u6807\u7684\u6700\u5927\u503c\uff08\u76f4\u63a5\u5199\u51fa\u7ed3\u679c\u5373\u53ef\uff09\uff0e
\u3010\u89e3\u7b54\u65b9\u6cd5\u3011
\u4e00\u3001\u5206\u6790
\uff081\uff09\u5229\u7528\u52fe\u80a1\u5b9a\u7406\u5373\u53ef\u6c42\u51faAE\u2032\uff0cBF\u2032\u7684\u957f\uff0e
\uff082\uff09\u8fd0\u7528\u5168\u7b49\u4e09\u89d2\u5f62\u7684\u5224\u5b9a\u4e0e\u6027\u8d28\u3001\u4e09\u89d2\u5f62\u7684\u5916\u89d2\u6027\u8d28\u5c31\u53ef\u89e3\u51b3\u95ee\u9898\uff0e
\uff083\uff09\u9996\u5148\u627e\u5230\u4f7f\u70b9P\u7684\u7eb5\u5750\u6807\u6700\u5927\u65f6\u70b9P\u7684\u4f4d\u7f6e\uff08\u70b9P\u4e0e\u70b9D\u2032\u91cd\u5408\u65f6\uff09\uff0c\u7136\u540e\u8fd0\u7528\u52fe\u80a1\u5b9a\u7406\u53ca30\u00b0\u89d2\u6240\u5bf9\u7684\u76f4\u89d2\u8fb9\u7b49\u4e8e\u659c\u8fb9\u7684\u4e00\u534a\u7b49\u77e5\u8bc6\u5373\u53ef\u6c42\u51fa\u70b9P\u7684\u7eb5\u5750\u6807\u7684\u6700\u5927\u503c\uff0e
\u89e3\uff1a\uff08\u2160\uff09\u5f53\u03b1=90\u00b0\u65f6\uff0c\u70b9E\u2032\u4e0e\u70b9F\u91cd\u5408\uff0c\u5982\u56fe\u2460\uff0e\u2235\u70b9A\uff08-2\uff0c0\uff09\u70b9B\uff080\uff0c2\uff09\uff0c\u2234OA=OB=2\uff0e\u2235\u70b9E\uff0c\u70b9F\u5206\u522b\u4e3aOA\uff0cOB\u7684\u4e2d\u70b9\uff0c\u2234OE=OF=1\u2235\u6b63\u65b9\u5f62OE\u2032D\u2032F\u2032\u662f\u6b63\u65b9\u5f62OEDF\u7ed5\u70b9O\u987a\u65f6\u9488\u65cb\u8f6c90\u00b0\u5f97\u5230\u7684\uff0c\u2234OE\u2032=OE=1\uff0cOF\u2032=OF=1\uff0e\u5728Rt\u25b3AE\u2032O\u4e2d\uff0c
\uff08\u2161\uff09\u5f53\u03b1=135\u00b0\u65f6\uff0c\u5982\u56fe\u2461\uff0e\u2235\u6b63\u65b9\u5f62OE\u2032D\u2032F\u2032\u662f\u7531\u6b63\u65b9\u5f62OEDF\u7ed5\u70b9O\u987a\u65f6\u9488\u65cb\u8f6c135\u00b0\u6240\u5f97\uff0c\u2234\u2220AOE\u2032=\u2220BOF\u2032=135\u00b0\uff0e\u5728\u25b3AOE\u2032\u548c\u25b3BOF\u2032\u4e2d\uff0c
\uff08\u2162\uff09\u5728\u7b2c\u4e00\u8c61\u9650\u5185\uff0c\u5f53\u70b9D\u2032\u4e0e\u70b9P\u91cd\u5408\u65f6\uff0c\u70b9P\u7684\u7eb5\u5750\u6807\u6700\u5927\uff0e\u8fc7\u70b9P\u4f5cPH\u22a5x\u8f74\uff0c\u5782\u8db3\u4e3aH\uff0c\u5982\u56fe\u2462\u6240\u793a\uff0e\u2235\u2220AE\u2032O=90\u00b0\uff0cE\u2032O=1\uff0cAO=2\uff0c
\uff081\uff094\uff0c\u89e3\uff1a\u5982\u56fe1\uff0c\u2235AC\u3001DC\u5173\u4e8e\u76f4\u7ebfBC\u5bf9\u79f0\uff0c\u2234AC=DC=4\uff0e\uff082\uff09\u89e3\uff1a\u5982\u56fe2\uff0c\u2235\u56db\u8fb9\u5f62A\u2032CBD\u662f\u6b63\u65b9\u5f62\uff0c\u2234A\u2032C=BC\uff0c\u2235A\u2032\u662fA\u5173\u4e8e\u76f4\u7ebfBC\u7684\u5bf9\u79f0\u70b9\uff0c\u2234AC=A\u2032C\uff0c\u2220ACB=90\u00b0\uff0c\u2234AC=BC\uff0c\u2234\u25b3ABC\u662f\u7b49\u8170\u76f4\u89d2\u4e09\u89d2\u5f62\uff0c\u4f5cCF\u22a5AB\uff0c\u2234B\uff084\uff0c0\uff09\u2234AF=BF=12AB=2\uff0c\u2235E\uff080\uff0c2\uff09\u2234CF=2\uff0c\u2234C\uff082\uff0c2\uff09\uff0e
解：（Ⅰ）当α=90°时，点E′与点F重合，如图①．∵点A（-2，0）点B（0，2），
∴OA=OB=2．
∵点E，点F分别为OA，OB的中点，
∴OE=OF=1
∵正方形OE′D′F′是正方形OEDF绕点O顺时针旋转90°得到的，
∴OE′=OE=1，OF′=OF=1．
在Rt△AE′O中，
AE′=
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