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<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">如图，在平面直角坐标系中，四边形</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">ABCD</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">为菱形，且点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">D</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（﹣</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">4</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">0</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">）在</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">x</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">轴上，点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">B</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">和点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">C</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">0</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">3</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">）在</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">y</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">轴上，反比例函数</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">y=</span></span></span></span></span><img height="35" src="/uploads/meth/20201224/a938f5d50d95af7f7519f0d37c7583cc.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">k</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">≠</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">0</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">）过点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">A</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">E</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（﹣</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">2</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">m</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">）、点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">F</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">分别是反比例函数图象上的点，其中点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">F</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">在第一象限，连结</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">OE</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">、</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">OF</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，以线段</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">OE</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">、</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">OF</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">为邻边作平行四边形</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">OEGF</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">．</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">1</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">）写出反比例函数的解析式；</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">2</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">）当点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">A</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">、</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">O</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">、</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">F</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">在同一直线上时，求出点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">G</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">的坐标；</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">3</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">）四边形</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">OEGF</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">周长是否有最小值？若存在，求出这个最值，并确定此时点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">F</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">的坐标，若不存在，请说明理由．</span></span></span></span></span></span><br /> <img height="174" src="/uploads/meth/20201224/b5ed32c45956323c91e5852bc94ab051.png" width="177" />
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<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">解：（</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">1</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">）</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∵</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">D</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（﹣</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">4</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">0</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">）在</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">x</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">轴上，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∴</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">A</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">点横坐标为：﹣</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">4</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∵</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">C</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">0</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">3</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">）在</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">y</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">轴上，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∴</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">DC=5</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∵</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">四边形</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">ABCD</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">为菱形，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∴</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">AD=5</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∴</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">A</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">的坐标为（﹣</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">4</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，﹣</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">5</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">），</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">则解析式为：</span></span></span></span></span></span><img height="35" src="/uploads/meth/20201224/eb693347988d6790157593de34dd5ebf.png" width="39" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">；</span></span></span></span></span></span><br /> <br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">2</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">）如图，</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∵</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">x=</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">﹣</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">2</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">时，</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">y=</span></span></span></span></span><img height="35" src="/uploads/meth/20201224/aef36ff9205e16524c730e8d0c84fe4b.png" width="21" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%">=</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">﹣</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">10</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∴</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">E</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">的坐标为（﹣</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">2</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，﹣</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">10</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">），</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∵</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">A</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">、</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">O</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">、</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">F</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">在同一直线上，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∴</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">A</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">F</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">关于原点对称，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∴</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">F</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">的坐标（</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">4</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">5</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">），</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">分别过点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">E</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">、</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">F</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">作</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">EN</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">⊥</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">x</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">轴于点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">N</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">FM</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">⊥</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">GM</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">于点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">M</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">FM</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">也垂直于</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">x</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">轴，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∵</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">四边形</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">OEGF</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">是平行四边形，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∴</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">EO</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∥</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">FG</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∴∠</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">NOE=</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∠</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">3</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∵∠</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">2=</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∠</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">3=</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∠</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">1</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∴∠</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">1=</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∠</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">NOE</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">在</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">△</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">ENO</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">和</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">△</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">FMG</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">中</span></span></span></span></span></span><br /> <img height="60" src="/uploads/meth/20201224/1817b7125372020375e30a7cf006344a.png" width="100" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">∴△</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">ENO</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">≌△</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">FMG</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">AAS</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">），</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">设点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">G</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">的坐标为（</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">m</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">n</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">），则</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">5</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">﹣</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">n=10</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">m</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">﹣</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">4=</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">﹣</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">2</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">故</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">n=</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">﹣</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">5</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">m=2</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">则点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">G</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">的坐标为（</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">2</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，﹣</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">5</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">）；</span></span></span></span></span></span><br /> <br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">（</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">3</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">）由于</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">OE</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">为定值，则只需求出</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">OF</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">的最小值即可，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">设点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">F</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">的坐标为（</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">a</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span></span><img height="35" src="/uploads/meth/20201224/8a05b2156a5aaa46c8076a108e47e151.png" width="21" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">），</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">根据勾股定理得，</span></span></span></span></span></span><img height="46" src="/uploads/meth/20201224/a8c08b7a6e6ecdd93479e8d323d22521.png" width="196" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">显然当</span></span></span></span></span></span><img height="35" src="/uploads/meth/20201224/9226a06fda13f6dfe5374a6596d80122.png" width="39" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">．时，</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">OF<sup>2</sup></span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">最小，即</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">a=2</span></span></span></span></span><img height="18" src="/uploads/meth/20201224/f5e1ad93d051169e73ab37c62691befe.png" width="20" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">时，</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">OF</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">最小，</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">OF=2</span></span></span></span></span><img height="18" src="/uploads/meth/20201224/3dcab373a9bb6eae0daf24391f624bda.png" width="28" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%">EO=2</span></span></span></span></span><img height="18" src="/uploads/meth/20201224/0e6bf354bf0291fb886acd35e1c3548c.png" width="28" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">因此，当点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">F</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">的坐标为（</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">2</span></span></span></span></span><img height="18" src="/uploads/meth/20201224/35998ddea3ab8a632e8adb9b19ceb0e8.png" width="20" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">2</span></span></span></span></span><img height="18" src="/uploads/meth/20201224/5719dc9907733a9655459b79313c9484.png" width="20" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">）时，四边形</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">OEGF</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">周长最小，</span></span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">最小值为：</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">4</span></span></span></span></span><img height="18" src="/uploads/meth/20201224/7c343cf9f773f686c550d95dfe6e8e2f.png" width="28" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">+</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">4</span></span></span></span></span><img height="18" src="/uploads/meth/20201224/eebbc282e405c4a2d1c99cea5c623e55.png" width="28" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">．</span></span></span></span></span></span><br /> <img height="174" src="/uploads/meth/20201224/2098bca7c57c61400421363fe029f18b.png" width="177" />
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