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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，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/e1ffe4d9a0ea995265592f917681e410.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">）的图象与正比例函数</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">y=kx</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></span></span><img height="35" src="/uploads/meth/20201224/b382216bc92e58cdb9ee5a8cf05098e6.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%">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%">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">）的图象分别交于点</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%">B</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">．若</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%">AOB=45°</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%"><span style="font-family:宋体">△</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">AOB</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">的面积是<u>　    </u></span></span></span><u>　</u><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/acdf1527dff59371d1b07d31ee926e87.png" width="181" />

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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，过</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">作</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">BD</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%">D</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，过</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%">AC</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">轴于点</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">C</span></span></span></span></span><br />
<img height="196" src="/uploads/meth/20201224/e0283dae95477631151d8c4f05951d7b.png" width="226" /><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%">A</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">横坐标为</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">，则</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%">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/20201224/48a4cac75dc1e639a91030836afa7c58.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%">A</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">在正比例函数</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">y=kx</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">图象上</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></span></span><img height="35" src="/uploads/meth/20201224/07150550c7590e46bd553a0a5ce3ed5d.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%">=ka</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></span></span><img height="41" src="/uploads/meth/20201224/2a9029477c8ab6d1f154a6f9fa55364c.png" width="22" /><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">同理，设点</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">横坐标为</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">，则</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">（</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">，</span></span></span></span></span></span><img height="35" src="/uploads/meth/20201224/79898e150d7957ab766ad4496995840c.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></span></span><img height="35" src="/uploads/meth/20201224/925a50cc07e39ffd249ce797474da66a.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></span></span></span></span><img height="35" src="/uploads/meth/20201224/6c4034fce1296585b73e0fcc3b566f82.png" width="23" /><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></span></span><img height="41" src="/uploads/meth/20201224/025affef580fd960b86647a9ff7030d5.png" width="40" /><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></span></span><img height="46" src="/uploads/meth/20201224/785dcda3f613e6a4f074ee24d93e53de.png" width="53" /><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%">ab=2</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">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">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/20201224/9c6017de790f7acad41b669bd341a53b.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">）时，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">坐标为（</span></span></span></span></span></span><img height="35" src="/uploads/meth/20201224/5f78ec0f747feff7439151d6ff2fd7ed.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%">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 />
<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%">OC=OD</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">将</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%">AOC</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">绕点</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">顺时针旋转</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">90°</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">，得到</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%">ODA′</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%">BD</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</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</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%">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%">A′</span></span><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">共线</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 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%">AOA′=90°</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%">BOA′=45°</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%">OA=OA′</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%">OB=OB</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</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%">A′OB</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%">S</span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">△</span></span></span></sub><sub><span style="font-size:12.0pt"><span style="line-height:150%">BOD</span></span></sub><span style="font-size:12.0pt"><span style="line-height:150%">=S</span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">△</span></span></span></sub><sub><span style="font-size:12.0pt"><span style="line-height:150%">AOC</span></span></sub><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><img height="35" src="/uploads/meth/20201224/120e6d8eeba85e9c44ce41c63cf9b213.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%">=1</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%">S</span></span><sub><span style="font-size:12.0pt"><span style="line-height:150%"><span style="font-family:宋体">△</span></span></span></sub><sub><span style="font-size:12.0pt"><span style="line-height:150%">AOB</span></span></sub><span style="font-size:12.0pt"><span style="line-height:150%">=2</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">故答案为：</span></span></span><span style="font-size:12.0pt"><span style="line-height:150%">2</span></span></span></span></span>

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