从点(x 1,y 1)到直线ax + by + c = 0的垂直距离是
|(ax 1 + by 1 + c)/ √ [a 2 + b 2 ] |
例1:
查找从(2,-3)到直线的垂直线的长度2x-y + 9 = 0
解决方案:
从点(x 1,y 1)到线ax + by + c = 0的垂线长度为
|(ax 1 + by 1 + c)/ √ [a 2 + b 2 ] |
替代。
= | [2(2)-(-3)+ 9] / √[ 2 2 +(-1)2 ] |
= |(4 + 3 + 9)/ √(4 +1)|
= | 16 / √5 |
= 16 / √5个单位
例2:
找到从(5,2)到直线3x + 2y-1 = 0的垂直线的长度
解决方案:
从点(x 1,y 1)到直线ax + by + c = 0的垂线长度为
|(ax 1 + by 1 + c)/ √ [a 2 + b 2 ] |
替代。
= | [3(5)+ 2(2)-1] / √[3 2 + 2 2 ] |
= | [15 + 4-1 ] / √[9 + 4] |
= | 18 / √13 |
= 18 / √13 单位
例3:
找到从(0,1)到直线x-3y + 2 = 0的垂线的长度
解决方案:
从点(x 1,y 1)到直线ax + by + c = 0的垂线长度为
|(ax 1 + by 1 + c)/ √ [a 2 + b 2 ] |
替代。
= | [1(0)-3(1)+ 2] / √[1 2 +(-3)2 ] |
= | [0-3 + 2] / √[1 + 9] |
= | -1 / √10 |
= 1 / √10个 单位
更新:20210423 104205