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1、Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.1 1 斜率存在时两直线平行斜率存在时两直线平行Evaluation only.Evaluation only. Created with
2、Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.结论结论1:1: 如果直线L1,L2的斜率为k1,k2 那么 L1L2 k1=k2 注意注意: :上面的等价是在两直线斜率存在的前提下才上面的等价是在两直线斜率存在的前提下才 成立的，缺少这个前提，结论并不成立成立的，缺少这个前提，
3、结论并不成立特殊情况下的两直线平行特殊情况下的两直线平行: :两直线的斜率都不存在时，互相平行两直线的斜率都不存在时，互相平行. .Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.如果直线
4、L1,L2的方程为L1:A1x+B1y+C1=0,L2:A2x+B2y+C2=0那么L1L2 = =212121 CC BB AA=212121 CCBBAA= Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspo
5、se Pty Ltd.例题讲解例题讲解 例例1 1Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.由例由例1 1所证结论，我们把与直线所证结论，我们把与直线 Ax+By+C=0Ax+By+
6、C=0平行的直线方程平行的直线方程 表示成表示成Ax+By+Ax+By+D D=0 =0 （D CD C） ， 其中其中D D待定待定（平行直线系）（平行直线系）结论结论2 2：同样可证明与直线同样可证明与直线y=kx+by=kx+b平行的平行的 直线可表示为直线可表示为y= kx+y= kx+Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5
7、.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.例2.求通过下列各点且与已知 直线平行的直线方程。Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Co
8、pyright 2004-2011 Aspose Pty Ltd.1 1 若直线若直线 和和 平行，则平行，则 = = 。a12=- ayx122=- ayx0 02 2 若直线若直线 和和 平行，则平行，则 = = 。a1+=+ayax22 +=+aayx1 1046=+-Cyx012=-yAx3 3 直线直线 和直线和直线 平行平行的条件是的条件是 。Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slide
9、s for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.4.设三条直线（1 1）若三条直线交于一点，求）若三条直线交于一点，求k k的值；的值；（2 2）若三条直线不能构成三角形，求）若三条直线不能构成三角形，求k k的值的值. .Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created
10、 with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.2 2 斜率存在时两直线垂直斜率存在时两直线垂直Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profil
11、e 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.结论结论3 3：如果两直线的斜率为k1, k2,那么,这两条直线垂直 k1k2= -1注意注意: :上面的等价是在两直线斜率存在的前提下才成立的，上面的等价是在两直线斜率存在的前提下才成立的，缺少这个前提，结论并不成立缺少这个前提，结论并不成立特殊情况下的两直线垂直特殊情况下的两直线垂直当两条直线中有一条直线斜率不存在，另一条当两条直线中有一条直线斜率不存在，另一条 直线的斜率为直线的斜率为0 0时，两直线垂直。时，两直线垂直。Eva
12、luation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.如果直线L1,L2的方程为L1:A1x+B1y+C1=0,L2:A2x+B2y+C2=0.那么L1L2 A1A2+B1B2=0Evaluation
13、 only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.例3.判断下列各组中的两条直线是否垂直（1）2x-4y-7=0与2x+y-5=0（2 2）y=3x+1y=3x+1与与y= x+5y= x+5（3 3）2x2x
14、7 7与与3y-5=03y-5=0Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.例4.求证：直线Ax+By+ =0与 直线 Bx-Ay+ =0垂直.证明：因为证明：因为ABABB(-A)
15、B(-A)0 0所以这两条直线垂直所以这两条直线垂直Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.一般地，我们把与直线一般地，我们把与直线Ax+By+C=0Ax+By+C=0垂直垂直 的直线方程表示为的直线方程表示为Bx-Ay+Bx-Ay+D D=0 =0 ，其中，其中D
