2d 中点和直线的垂直距离
给定点(x1，y1)和直线(ax + by + c = 0)。任务是找到给定点和直线之间的垂直距离。
例:
输入: x1 = 5，y1 = 6，a = -2，b = 3，c = 4 输出: 3.32820117735 输入: x1 = -1，y1 = 3，a = 4，b = -3，c =–5 输出: 3.6
进近:从给定点到一条线的距离(即最短距离)是从该点到给定线的垂直距离。平面中直线的方程由方程 ax + by + c = 0 给出，其中 a、b 和 c 是实常数。点的坐标是(x1，y1) 二维空间中点和线之间的距离公式如下:
Distance = (| a*x1 + b*y1 + c |) / (sqrt( a*a + b*b))
以下是上述公式的实现: 程序 1:
C
// C program to find the distance
// between a given point and a
// given line in 2 D.
#include<stdio.h>
#include<math.h>
// Function to find distance
void shortest_distance(float x1, float y1,
float a, float b,
float c)
{
float d = fabs((a * x1 + b * y1 + c)) /
(sqrt(a * a + b * b));
printf("Perpendicular distance is %f\n", d);
return;
}
// Driver Code
int main()
{
float x1 = 5;
float y1 = 6;
float a = -2;
float b = 3;
float c = 4;
shortest_distance(x1, y1, a, b, c);
return 0;
}
// This code is contributed
// by Amber_Saxena.
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to find
// the distance between
// a given point and a
// given line in 2 D.
import java.io.*;
class GFG
{
// Function to find distance
static void shortest_distance(float x1, float y1,
float a, float b,
float c)
{
double d = Math.abs(((a * x1 + b * y1 + c)) /
(Math.sqrt(a * a + b * b)));
System.out.println("Perpendicular " +
"distance is " + d);
return;
}
// Driver code
public static void main (String[] args)
{
float x1 = 5;
float y1 = 6;
float a = -2;
float b = 3;
float c = 4;
shortest_distance(x1, y1, a, b, c);
}
}
// This code is contributed
// by Mahadev.
计算机编程语言
# Python program to find the distance between
# a given point and a given line in 2 D.
import math
# Function to find distance
def shortest_distance(x1, y1, a, b, c):
d = abs((a * x1 + b * y1 + c)) / (math.sqrt(a * a + b * b))
print("Perpendicular distance is"),d
# Driver Code
x1 = 5
y1 = 6
a = -2
b = 3
c = 4
shortest_distance(x1, y1, a, b, c)
C
// C# program to find
// the distance between
// a given point and a
// given line in 2 D.
using System;
class GFG
{
// Function to find distance
static void shortest_distance(float x1, float y1,
float a, float b,
float c)
{
double d = Math.Abs(((a * x1 + b * y1 + c)) /
(Math.Sqrt(a * a + b * b)));
Console.WriteLine("Perpendicular " +
"distance is " + d);
return;
}
// Driver code
public static void Main ()
{
float x1 = 5;
float y1 = 6;
float a = -2;
float b = 3;
float c = 4;
shortest_distance(x1, y1, a, b, c);
}
}
// This code is contributed
// by inder_verma..
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP program to find the distance
// between a given point and a
// given line in 2 D.
// Function to find distance
function shortest_distance($x1, $y1, $a, $b, $c)
{
$d = abs(($a * $x1 + $b * $y1 + $c)) /
(sqrt($a * $a + $b * $b));
echo"Perpendicular distance is ", $d;
}
// Driver Code
$x1 = 5;
$y1 = 6;
$a = -2;
$b = 3;
$c = 4;
shortest_distance($x1, $y1, $a, $b, $c);
// This code is contributed
// by inder_verma..
?>
java 描述语言
<script>
// Javascript program to find
// the distance between
// a given point and a
// given line in 2 D.
// Function to find distance
function shortest_distance(x1 , y1 , a , b , c)
{
var d = Math.abs((
(a * x1 + b * y1 + c)) / (Math.sqrt(a * a + b * b)));
document.write("Perpendicular " +
"distance is " + d.toFixed(11));
return;
}
// Driver code
var x1 = 5;
var y1 = 6;
var a = -2;
var b = 3;
var c = 4;
shortest_distance(x1, y1, a, b, c);
// This code is contributed by todaysgaurav
</script>
Output:
Perpendicular distance is 3.32820117735
节目 2 :
C
// C program to find the distance
// between a given point and a
// given line in 2 D.
#include<stdio.h>
#include<math.h>
// Function to find distance
void shortest_distance(float x1, float y1,
float a, float b,
float c)
{
float d = fabs((a * x1 + b * y1 + c)) /
(sqrt(a * a + b * b));
printf("Perpendicular distance is %f\n", d);
return;
}
// Driver Code
int main()
{
float x1 = -1;
float y1 = 3;
float a = 4;
float b = -3;
float c = - 5;
shortest_distance(x1, y1, a, b, c);
return 0;
}
// This code is contributed
// by Amber_Saxena.
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to find the distance
// between a given point and a
// given line in 2 D.
class GFG
{
// Function to find distance
static void shortest_distance(double x1, double y1,
double a, double b,
double c)
{
double d = Math.abs((a * x1 + b * y1 + c)) /
(Math.sqrt(a * a + b * b));
System.out.println("Perpendicular distance is " + d);
return;
}
// Driver Code
public static void main(String[] args)
{
double x1 = -1;
double y1 = 3;
double a = 4;
double b = -3;
double c = - 5;
shortest_distance(x1, y1, a, b, c);
}
}
// This code is contributed
// by mits
计算机编程语言
# Python program to find the distance between
# a given point and a given line in 2 D.
import math
# Function to find distance
def shortest_distance(x1, y1, a, b, c):
d = abs((a * x1 + b * y1 + c)) / (math.sqrt(a * a + b * b))
print("Perpendicular distance is"),d
# Driver Code
x1 = -1
y1 = 3
a = 4
b = -3
c = - 5
shortest_distance(x1, y1, a, b, c)
C
// C# program to find the distance
// between a given point and a
// given line in 2 D.
using System;
class GFG
{
// Function to find distance
static void shortest_distance(double x1, double y1,
double a, double b,
double c)
{
double d = Math.Abs((a * x1 + b * y1 + c)) /
(Math.Sqrt(a * a + b * b));
Console.WriteLine("Perpendicular distance is " + d);
return;
}
// Driver Code
public static void Main()
{
double x1 = -1;
double y1 = 3;
double a = 4;
double b = -3;
double c = - 5;
shortest_distance(x1, y1, a, b, c);
}
}
// This code is contributed
// by Akanksha Rai
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP program to find the distance
// between a given point and a
// given line in 2 D.
// Function to find distance
function shortest_distance($x1, $y1, $a,
$b, $c)
{
$d = abs((int)($a * $x1 + $b * $y1 + $c) /
sqrt($a * $a + $b * $b));
echo"Perpendicular distance is ", $d;
}
// Driver Code
$x1 = -1;
$y1 = 3;
$a = 4;
$b = -3;
$c = -5;
shortest_distance($x1, $y1, $a, $b, $c);
// This code is contributed
// by inder_verma..
?>
java 描述语言
<script>
// Javascript program to find the distance
// between a given point and a
// given line in 2 D.
// Function to find distance
function shortest_distance(x1, y1, a, b, c)
{
let d = Math.abs((a * x1 + b * y1 + c)) /
(Math.sqrt(a * a + b * b));
document.write("Perpendicular distance is " + d);
return;
}
// driver program
let x1 = -1;
let y1 = 3;
let a = 4;
let b = -3;
let c = - 5;
shortest_distance(x1, y1, a, b, c);
// This code is contributed by susmitakundugoaldanga.
</script>
Output:
Perpendicular distance is 3.6
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