Program to find the Centroid of the triangle
Given the vertices of the triangle. The task is to find the centroid of the triangle:
Examples:
Input: A(1, 2), B(3, -4), C(6, -7)
Output: (3.33, -3)
Input: A(6, 2), B(5, -9), C(2, -7)
Output: (6.5, -9)
Approach:Suppose if the vertices of a triangle are (x1, y1) (x2, y2) (x3, y3) then centroid of the triangle can be find from the following formula:
[Tex]$$ X = \frac{x_{1}+x_{2}+x_{3}}{2} $$ $$ Y = \frac{y_{1}+y_{2}+y_{3}}{2} $$ [/Tex]
1. Set x1, y1, x2, y2, x3, y3 to the coordinates of the vertices of the triangle.
2. Calculate the average x-coordinate of the vertices as x = (x1 + x2 + x3) / 3.
3. Calculate the average y-coordinate of the vertices as y = (y1 + y2 + y3) / 3.
4. Print "Centroid = (" + x + ", " + y + ")".
// CPP program to find the centroid of triangle
#include <bits/stdc++.h>
using namespace std;
// Driver code
int main()
{
// coordinate of the vertices
float x1 = 1, x2 = 3, x3 = 6;
float y1 = 2, y2 = -4, y3 = -7;
// Formula to calculate centroid
float x = (x1 + x2 + x3) / 3;
float y = (y1 + y2 + y3) / 3;
cout << setprecision(3);
cout << "Centroid = "
<< "(" << x << ", " << y << ")";
return 0;
}
// Java program to find the centroid of triangle
import java.util.*;
import java.lang.*;
class GFG
{
// Driver code
public static void main(String args[])
{
// coordinate of the vertices
float x1 = 1, x2 = 3, x3 = 6;
float y1 = 2, y2 = -4, y3 = -7;
// Formula to calculate centroid
float x = (x1 + x2 + x3) / 3;
float y = (y1 + y2 + y3) / 3;
//System.out.print(setprecision(3));
System.out.println("Centroid = "
+ "(" + x + ", " + y + ")");
}
}
// This code is contributed
// by Akanksha Rai(Abby_akku)
# Python3 program to find
# the centroid of triangle
# Driver code
if __name__ == "__main__" :
# coordinate of the vertices
x1, x2, x3 = 1, 3, 6
y1, y2, y3 = 2, -4, -7
# Formula to calculate centroid
x = round((x1 + x2 + x3) / 3, 2)
y = round((y1 + y2 + y3) / 3, 2)
print("Centroid =","(",x,",",y,")")
# This code is contributed by ANKITRAI1
// C# program to find the
// centroid of triangle
using System;
class GFG
{
// Driver code
static public void Main ()
{
// coordinate of the vertices
float x1 = 1, x2 = 3, x3 = 6;
float y1 = 2, y2 = -4, y3 = -7;
// Formula to calculate centroid
float x = (x1 + x2 + x3) / 3;
float y = (y1 + y2 + y3) / 3;
//System.out.print(setprecision(3));
Console.Write("Centroid = " +
"(" + x + ", " + y + ")");
}
}
// This code is contributed
// by RaJ
<script>
// javascript program to find the centroid of triangle
// Driver code
// coordinate of the vertices
var x1 = 1, x2 = 3, x3 = 6;
var y1 = 2, y2 = -4, y3 = -7;
// Formula to calculate centroid
var x = (x1 + x2 + x3) / 3;
var y = (y1 + y2 + y3) / 3;
// document.write(setprecision(3));
document.write("Centroid = "
+ "(" + x.toFixed(2) + ", " + y + ")");
// This code contributed by shikhasingrajput
</script>
<?php
// PHP program to find the
// centroid of triangle
// Driver code
// coordinate of the vertices
$x1 = 1;
$x2 = 3 ;
$x3 = 6;
$y1 = 2;
$y2 = -4;
$y3 = -7;
// Formula to calculate centroid
$x = round(($x1 + $x2 + $x3) / 3, 2);
$y = round(($y1 + $y2 + $y3) / 3, 2);
echo "Centroid = " .
"(" .$x .", " .$y .")";
// This code is contributed
// by ChitraNayal
?>
Output
Centroid = (3.33, -3)
Time complexity: O(1), since there is no loop or recursion.
Auxiliary Space: O(1), since no extra space has been taken.
New Approach:
Another approach to find the centroid of a triangle is to use the concept of vectors.
- Let the vertices of the triangle be A(x1, y1), B(x2, y2), and C(x3, y3).
- Then, the centroid G can be found using the following formula: G = (A + B + C) / 3 where A, B, and C are position vectors of the respective vertices. In other words, G = ((x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3)
Below is the code for the above approach :
// C++ program to find the centroid of a triangle
#include <iostream>
using namespace std;
// Structure to store coordinates of a point
struct Point {
float x, y;
};
// Function to find the centroid of a triangle
Point findCentroid(Point A, Point B, Point C)
{
float x = (A.x + B.x + C.x) / 3;
float y = (A.y + B.y + C.y) / 3;
Point G = { x, y };
return G;
}
// Driver code
int main()
{
// Coordinates of the vertices
Point A = { 1, 2 }, B = { 3, -4 }, C = { 6, -7 };
// Find the centroid of the triangle
Point G = findCentroid(A, B, C);
// Print the centroid
cout << "Centroid = (" << G.x << ", " << G.y << ")"
<< endl;
return 0;
}
// Java program to find the centroid of a triangle
import java.util.*;
// Class to store coordinates of a point
class Point {
float x, y;
Point(float x, float y) {
this.x = x;
this.y = y;
}
}
// Class to find the centroid of a triangle
class Centroid {
static Point findCentroid(Point A, Point B, Point C) {
float x = (A.x + B.x + C.x) / 3;
float y = (A.y + B.y + C.y) / 3;
Point G = new Point(x, y);
return G;
}
// Driver code
public static void main(String[] args) {
// Coordinates of the vertices
Point A = new Point(1, 2), B = new Point(3, -4), C = new Point(6, -7);
// Find the centroid of the triangle
Point G = findCentroid(A, B, C);
// Print the centroid
System.out.println("Centroid = (" + G.x + ", " + G.y + ")");
}
}
# Python3 program to find the centroid of a triangle
import math
# Structure to store coordinates of a point
class Point:
def __init__(self, x, y):
self.x = x
self.y = y
# Function to find the centroid of a triangle
def findCentroid(A, B, C):
x = (A.x + B.x + C.x) / 3
y = (A.y + B.y + C.y) / 3
G = Point(round(x, 6), round(y, 6))
return G
# Driver code
if __name__ == "__main__":
# Coordinates of the vertices
A = Point(1, 2)
B = Point(3, -4)
C = Point(6, -7)
# Find the centroid of the triangle
G = findCentroid(A, B, C)
# Print the centroid
print("Centroid = ({}, {})".format(G.x, G.y))
// C# program to find the centroid of a triangle
using System;
// Structure to store coordinates of a point
struct Point
{
public float x;
public float y;
}
// Class to find the centroid of a triangle
class Centroid {
// Function to find the centroid of a triangle
public static Point findCentroid(Point A, Point B,
Point C)
{
float x = (A.x + B.x + C.x) / 3;
float y = (A.y + B.y + C.y) / 3;
Point G = new Point{ x = x, y = y };
return G;
}
// Driver code
static void Main(string[] args)
{
// Coordinates of the vertices
Point A = new Point{ x = 1, y = 2 };
Point B = new Point{ x = 3, y = -4 };
Point C = new Point{ x = 6, y = -7 };
// Find the centroid of the triangle
Point G = findCentroid(A, B, C);
// Print the centroid
Console.WriteLine("Centroid = ({0}, {1})", G.x,
G.y);
}
}
// This code is contributed by sarojmcy2e
// Class to store coordinates of a point
class Point {
constructor(x, y) {
this.x = x;
this.y = y;
}
}
// Class to find the centroid of a triangle
class Centroid {
static findCentroid(A, B, C) {
let x = (A.x + B.x + C.x) / 3;
let y = (A.y + B.y + C.y) / 3;
let G = new Point(x, y);
return G;
}
// Driver code
static main() {
// Coordinates of the vertices
let A = new Point(1, 2), B = new Point(3, -4), C = new Point(6, -7);
// Find the centroid of the triangle
let G = Centroid.findCentroid(A, B, C);
// Print the centroid
console.log(`Centroid = (${G.x}, ${G.y})`);
}
}
// Call the main method
Centroid.main();
Output
Centroid = (3.33333, -3)
Time complexity: O(1), as the calculations involved are simple arithmetic operations.
Auxiliary Space: O(1), as the only variables used are the coordinates of the vertices and the centroid, which require constant space.
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