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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，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/20201224/0a803932bbdabceb391dbe7d20deac8d.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%">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%">0</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">）的图象经过点</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">（﹣</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%">1</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">作</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">AB</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%">y</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">轴，垂足为</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">，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">轴的正半轴上取一点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">P</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%">t</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%">P</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">作直线</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">OA</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">的垂线</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">l</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，以直线</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">l</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">为对称轴，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">经轴对称变换得到的点</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">在此反比例函数的图象上，则</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">t</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">的值是（　　）</span></span></span></span></span></span><br />
                                                                                                                                                   <img height="154" src="/uploads/meth/20201224/92fa0a07cbc3e991d84faee5804e4f8f.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：如图，                                         </span></span></span></span></span></span><img height="154" src="/uploads/meth/20201224/c92a81d57af5e598475205da4f3e3b6e.png" width="177" /><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">坐标为（﹣</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%">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%">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%">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%">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%">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%"><span style="font-family:宋体">反比例函数解析式为</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">﹣</span></span></span></span></span></span><img height="35" src="/uploads/meth/20201224/33fc432390dbf07936b791eb248f7f5e.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></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%">OB=AB=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%">OAB</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">为等腰直角三角形，</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%">AOB=45°</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%">PQ</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%">OA</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%">OPQ=45°</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%">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%">B′</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">关于直线</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">l</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">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%">PB=PB′</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%">BB′</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%">PQ</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%">B′PQ=</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%">OPQ=45°</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%">B′PB=90°</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%">B′P</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%">y</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">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">的坐标为（﹣</span></span></span></span></span></span><img height="35" src="/uploads/meth/20201224/fa7325110fdf9bfff28fefdbf6899911.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%">t</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%">PB=PB′</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%">t</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 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/20201224/11cc237de68a049bac44e7bd6e1eebc0.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%">=</span></span></span></span></span><img height="35" src="/uploads/meth/20201224/a6cbd68be24be280598ce83c66656993.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></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">整理得</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">t<sup>2</sup></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%">t</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=0</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，解得</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">t<sub>1</sub>=</span></span></span></span></span><img height="37" src="/uploads/meth/20201224/2afea037b23a0358a380caddbb71b3b0.png" width="41" /><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%">t<sub>2</sub>=</span></span></span></span></span><img height="37" src="/uploads/meth/20201224/59ce292c114783a8d8766192bd4b98b2.png" width="41" /><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">（不符合题意，舍去），</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%">t</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">的值为</span></span></span></span></span></span><img height="37" src="/uploads/meth/20201224/84ca118483fcb0be9c7b6273a311d864.png" width="41" /><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">故选：</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><br />

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