两条平行线之间的距离

给定斜率为m 的两条平行直线，以及不同的 y 截距b1和b2 。任务是找到这两条平行线之间的距离。
例子：

Input: m = 2, b1 = 4, b2 = 3
Output: 0.333333

Input: m = -4, b1 = 11, b2 = 23
Output: 0.8

方法：

1. 设PQ和RS为平行线，方程为
   y = mx + b1
   y = mx + b2
2. 这两条线之间的距离是这些线与垂线的两个交点之间的距离。让该距离为d 。
3. 因此，垂直于PQ和RS的直线的方程可以是
   y = -x/m
4. 现在，分别用 PQ 和 RS 求解垂线以获得相交点(x1, y1) & (x2, y2) ，我们得到，
5. 从PQ ,
   y = mx + b1
   y = -x/m
   (x1, y1) = ( -b1*m/(m^2 + 1), b1/(m^2 + 1))
6. 从RS ,
   y = mx + b2
   y = -x/m
   (x2, y2) = ( -b2*m/(m^2 + 1), b2/(m^2 + 1))
7. 所以， d = (x1, y1) 和 (x2, y2) 之间的距离
   $d = \frac{\left | b2 - b1 \right |}{ sqrt( m^{2} + 1 ) }$

下面是上述方法的实现：

C++

// C++ program find the distance
// between two parallel lines
 
#include 
using namespace std;
 
// Function to find the distance
// between parallel lines
double dist(double m, double b1, double b2)
{
    double d = fabs(b2 - b1) / ((m * m) - 1);
    return d;
}
 
// Driver Code
int main()
{
    double m = 2, b1 = 4, b2 = 3;
    cout << dist(m, b1, b2);
    return 0;
}

Java

// Java program find the distance
// between two parallel lines
class GFG
{
     
// Function to find the distance
// between parallel lines
static double dist(double m,
                double b1, double b2)
{
    double d = Math.abs(b2 - b1) /
                    ((m * m) - 1);
    return d;
}
 
// Driver Code
public static void main(String[] args)
{
    double m = 2, b1 = 4, b2 = 3;
     System.out.println(dist(m, b1, b2));
}
}
 
// This code is contributed by Code_Mech.

Python3

# Python3 program find the distance
# between two parallel lines
 
# Function to find the distance
# between parallel lines
def dist(m, b1, b2):
    d = abs(b2 - b1) / ((m * m) - 1);
    return d;
 
# Driver Code
def main():
    m, b1, b2 =2,4, 3;
    print(dist(m, b1, b2));
if __name__ == '__main__':
    main()
 
# This code contributed by PrinciRaj1992

C#

// C# program find the distance
// between two parallel lines
using System;
 
class GFG
{
     
// Function to find the distance
// between parallel lines
static double dist(double m,
                   double b1, double b2)
{
    double d = Math.Abs(b2 - b1) /
                      ((m * m) - 1);
    return d;
}
 
// Driver Code
public static void Main()
{
    double m = 2, b1 = 4, b2 = 3;
    Console.Write(dist(m, b1, b2));
}
}
 
// This code is contributed by Akanksha Rai

Javascript

 
// javascript program find the distance
// between two parallel lines
 
     
// Function to find the distance
// between parallel lines
function dist(m, b1 , b2)
{
    var d = Math.abs(b2 - b1) /
                    ((m * m) - 1);
    return d;
}
 
// Driver Code
var m = 2, b1 = 4, b2 = 3;
document.write(dist(m, b1, b2).toFixed(5));
 
 
// This code contributed by Princi Singh
 

输出：

0.333333