centroid triangle calculator - step by step calculation, formula & solved example to find the mid or center point of 3 given points of a triangle (x_{1}, y_{1}), (x_{2}, y_{2}) & (x_{3}, y_{3}) on the multi-dimensional coordinate system or plane. It also known as geometric center or barycenter calculator.
Formula
Centroid of a triangle is a mid point of 3 endpoints on a multi-dimensional coordinate system or plane mathematically represented by the below formula
Solved Example
This below solved example let users to understand how the example values are being used in this calculation to find the centroid of a triangle.
Problem:
Find the midpoint of triangle having 3 endpoints (x_{1}, y_{1}) = (5, 6) , (x_{2}, y_{2}) = (7, 9) & (x_{3}, y_{3}) = (9, 12).
Solution:
Let (x_{1}, y_{1})) be (5, 6) , (x_{2}, y_{2}) be (7, 9) & (x_{3}, y_{3}) be (9, 12) be the three points of a triangle
Apply the values in the equation
= ((x_{1} + x_{2} + x_{3})/3 , (y_{1} + y_{2} + y_{2})/2)
= ((5 + 7 + 9)/3,(6 + 9 + 12)/3)
= (21/3, 27/3)
= (7, 9)
The centroid of a triangle for the given values is (7, 9).
The above centroid of a triangle calculator, formula & solved example may useful for users to understand, practice and verify such calculations online. Unlike most of the other calculators, it provides complete step by step calculation for each calculation users do by using this Geometry tool to find the mid point for the three triangle cornor coordinates (x_{1}, y_{1}), (x_{2}, y_{2}) & (x_{3}, y_{3})