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两条线垂直公式

更新时间： 2021-04-20 06:37:24

1、两直线垂直且斜率存在时则斜率之积为-1，即k1×k2=-1。

通用公式是A1A2+B1B2=0

2、两直线一般式垂直公式的证明：

设直线l1：A1x+B1y+C1=0，直线l2：A2x+B2y+C2=0

（必要性）∵l1⊥l2 ∴k1×k2=-1

∵k1=-B1/A1, k2=-B2/A2

∴(-B1/A1)(B2/A2)=-1 ∴（B1B2）/(A1A2)=-1

∴B1B2=-A1A2 ∴A1A2+B1B2=0

（充分性）∵A1A2+B1B2=0 ∴B1B2=-A1A2

∴（B1B2）(1/A1A2)=-1 ∴(B1/A1)(B2/A2)=-1

∴(-B1/A1)(-B2/A2)=-1 ∵k1=-B1/A1, k2=-B2/A2

∴k1×k2=-1∴l1⊥l2

关键词：垂直公式

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