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: 

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 + ")".

C++

// 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

// 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)

Python 3

# 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#

// 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

PHP

<?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
?>

Javascript

<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>

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.

1. Let the vertices of the triangle be A(x1, y1), B(x2, y2), and C(x3, y3).
2. 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)

Bellow is the code for the above approach :

C++

// 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;
}

Python3

# 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))

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.