直线l：y=-x+1，现有下列3个结论，①点P（2，-1）在直线l上；②若直线l与x轴，y轴分别交于A，B两点，则
\u5df2\u77e5\u76f4\u7ebfl\u8fc7\u70b9p(2,1)\uff0c\u4e14\u4e0eX\u8f74\u3001y\u8f74\u7684\u6b63\u534a\u8f74\u5206\u522b\u4ea4\u4e8eA\u3001B\u4e24\u70b9\uff0cO\u4e3a\u5750\u6807\u539f\u70b9\uff0c\u5219\u4e09\u8bbe\u8fc7\u70b9P\u7684\u76f4\u7ebf\u4e3ay-1=k(x-2)
x=0\uff0cy=1-2k
y=0\uff0cx=(2k-1)/k
A((2k-1)/k,0)B(0,1-2k)
S\u4e09\u89d2\u5f62AOB=1/2\u00d7\uff5c1-2k\uff5c\u00d7\uff5c(2k-1)/k\uff5c=\uff5c(2k-1)²/2k\uff5c=\uff5c(4k²-4k+1)/2k\uff5c
=\uff5c2k+1/2k-2\uff5c
\u56e0\u4e3a\u76f4\u7ebf\u8fc7\u70b9P\u89d2x\u8f74\u548cy\u8f74\u6b63\u534a\u8f74
\u90a3\u4e48k<0
\u6240\u4ee5S=2+(-2k)+1/(-2k)\u22652+2\u221a(-2k)[1/(-2k)]=2+2=4
\u5f53\u4e14\u4ec5\u5f53-2k=1/(-2k)\u5373k=-1/2\u65f6\uff0c\u53d6\u6700\u5c0f\u503c\uff0c\u6240\u4ee5S\u6700\u5c0f\u503c=4
k=1/2\u820d\u53bb
\u89e3\uff1a\u4ee4y=0\uff0c\u5f97x=-3/2\uff0e
\u2234A\u70b9\u5750\u6807\u4e3a\uff08-3/2\uff0c0\uff09\uff0e
\u4ee4x=0\uff0c\u5f97y=3\uff0e
\u2234B\u70b9\u5750\u6807\u4e3a\uff080\uff0c3\uff09\uff0e
\u8bbeP\u70b9\u5750\u6807\u4e3a\uff08x\uff0c0\uff09\uff0c\u4f9d\u9898\u610f\uff0c\u5f97x=\u00b13\uff0c
\u2234P\u70b9\u5750\u6807\u5206\u522b\u4e3aP1\uff083\uff0c0\uff09\u6216P2\uff08-3\uff0c0\uff09\uff0e
\u2234S\u25b3ABP1= 1/2\u00d7\uff083/2+3\uff09\u00d73= 27/4\uff0c
S\u25b3ABP2= 1/2\u00d7\uff083-3/2\uff09\u00d73=9/4\uff0c
\u2234\u25b3ABP\u7684\u9762\u79ef\u4e3a 27/4\u6216 9/4
| ①②③ |
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