给定两个坐标(x1,y1)和(x2,y2)以及m和n,找到将坐标(x1,y1)和(x2,y2)按比例m:n划分的划分的坐标
例子:
Input : x1 = 1, y1 = 0, x2 = 2 y2 = 5,
m = 1, n = 1
Output : (1.5, 2.5)
Explanation: co-ordinates (1.5, 2.5)
divides the line in ratio 1 : 1
Input : x1 = 2, y1 = 4, x2 = 4, y2 = 6,
m = 2, n = 3
Output : (2.8, 4.8)
Explanation: (2.8, 4.8) divides the line
in the ratio 2:3
截面公式告诉我们将给定线段分为两部分的点的坐标,以使它们的长度为m:n
C++
// CPP program to find point that divides
// given line in given ratio.
#include
using namespace std;
// Function to find the section of the line
void section(double x1, double x2, double y1,
double y2, double m, double n)
{
// Applying section formula
double x = ((n * x1) + (m * x2)) /
(m + n);
double y = ((n * y1) + (m * y2)) /
(m + n);
// Printing result
cout << "(" << x << ", ";
cout << y << ")" << endl;
}
// Driver code
int main()
{
double x1 = 2, x2 = 4, y1 = 4,
y2 = 6, m = 2, n = 3;
section(x1, x2, y1, y2, m, n);
return 0;
}
Java
// Java program to find point that divides
// given line in given ratio.
import java.io.*;
class sections {
static void section(double x1, double x2,
double y1, double y2,
double m, double n)
{
// Applying section formula
double x = ((n * x1) + (m * x2)) /
(m + n);
double y = ((n * y1) + (m * y2)) /
(m + n);
// Printing result
System.out.println("(" + x + ", " + y + ")");
}
public static void main(String[] args)
{
double x1 = 2, x2 = 4, y1 = 4,
y2 = 6, m = 2, n = 3;
section(x1, x2, y1, y2, m, n);
}
}
Python
# Python program to find point that divides
# given line in given ratio.
def section(x1, x2, y1, y2, m, n):
# Applying section formula
x = (float)((n * x1)+(m * x2))/(m + n)
y = (float)((n * y1)+(m * y2))/(m + n)
# Printing result
print (x, y)
x1 = 2
x2 = 4
y1 = 4
y2 = 6
m = 2
n = 3
section(x1, x2, y1, y2, m, n)
C#
// C# program to find point that divides
// given line in given ratio.
using System;
class GFG {
static void section(double x1, double x2,
double y1, double y2,
double m, double n)
{
// Applying section formula
double x = ((n * x1) + (m * x2)) /
(m + n);
double y = ((n * y1) + (m * y2)) /
(m + n);
// Printing result
Console.WriteLine("(" + x + ", " + y + ")");
}
// Driver code
public static void Main()
{
double x1 = 2, x2 = 4, y1 = 4,
y2 = 6, m = 2, n = 3;
section(x1, x2, y1, y2, m, n);
}
}
// This code is contributed by vt_m.
PHP
Javascript
输出:
(2.8, 4.8)
这是如何运作的?
From our diagram, we can see,
PS = x – x1 and RT = x2 – x
We are given,
PR/QR = m/n
Using similarity, we can write
RS/QT = PS/RT = PR/QR
Therefore, we can write
PS/RR = m/n
(x - x1) / (x2 - x) = m/n
From above, we get
x = (mx2 + nx1) / (m + n)
Similarly, we can solve for y.
参考:
http://doubleroot.in/lessons/coordinate-geometry-basics/section-formula/#.WjYXQvbhU8o