What is a Centroid?
Almost every closed geometrical shape has a specific point where all its weight lies. That point is normally called the Centroid of that figure.
Mathematically, we can write the centroid definition as “The point where a specific figure is balanced is called a Centroid”.
This specific point lies inside that figure and may be its central point. So, we can also say that it is the center of the figure where its weight lies, not the actual central point.
What is the Centroid theorem?
Like other parameters, a centroid also has some specific properties that can be summarized in the form of a theorem. The centroid theorem states that the lengths of lines on both sides of the centroid should be in a ratio of 2:1.
It means that one side of the line of the centroid will be double to the other side. In simple words, the centroid doesn’t cut the medians from the center but it cuts it from one of its sides. Mathematically, we can show the centroid theorem using the following example.
Suppose we have a triangle with vertices, “A”, “B”, and “C” with the midpoints “D”, “E”, and “F” while the centroid of that triangle is represented by point “P”. So, we can write the general theorem of centroid as
AP : PD = BP : PE = CP : PF = 2 : 1
The above statement shows that the sides written on the left side of the ratio will be double as compared to the sides written on the right side of the ratio. This is the actual statement of the centroid theorem that summarizes all its properties in a mathematical relation.
What is a Centroid of a triangle?
Generally, most of the students assume that a triangle only involves three sides with three angles. It is completely wrong! Because multiple other terms and lengths are also involved in this figure. One of those terms/parameters is a centroid where the whole triangle is considered to be balanced.
The centroid of a triangle is defined as the point where the medians of all its sides meet. It is considered the central point of any triangle too. It doesn’t matter whether you are dealing with a right triangle or a scalene triangle, you can find its centroid using some simple steps that we will discuss further.
How to find the Centroid of a Triangle?
The centroid of a triangle is the point that you can find practically as well as mathematically too. To find this point mathematically, you can use the centroid of a triangle formula given below.
Centroid of a Triangle = [(x1 + x2 + x33) ,(y1 + y2 + y33)]
In this formula, “x” and “y” are the coordinates of three points of a triangle respectively. You only have to put the values of the points and solve them using basic mathematical operations.
Where is the Centroid of a right triangle located?
The centroid of a right triangle is located inside this figure and it is the point where the medians of the triangle meet. As it is a specific type of triangle with a particular shape, it might be hard to find this point.
To make the process easier and faster, you can use our Centroid Calculator. This online maths calculator has been programmed for this calculation. You can locate the centroid of a right triangle within seconds using this advanced tool. Just enter the values and you will get the answer quickly with 100% accuracy.
Solved Example of Calculating the Centroid
If you are struggling with the concept of the centroid of a triangle and are unable to understand the calculation, you should check the following example. We have solved it just for your better understanding
example:
Find the centroid of a triangle if its vertices are: A(2, 1), B(4, 7), and C(6, 9).
Solution:
By using the above formula, we can easily find the centroid of this triangle.
Centroid of a Triangle = [(x1 + x2 + x33) ,(y1 + y2 + y33)]
= [(2 + 4 + 63) ,(1 + 7 + 93)]
After simplifying the equation, we get:
Centroid of a triangle = (4, 5)
Conclusion
You can easily find the centroid of any triangle using the above formula. It might be possible that you have cleared all your doubts after viewing the solved example. We have also shared the comprehensive overview of the centroid of a triangle to let you understand this parameter.
But if you are still looking for assistance, you should use the centroid of a triangle calculator. This tool will help you in solving your assignments as well as let you understand the solution properly.
FAQ
How do you find the centroid?
To find the centroid of any figure, we need to use different formulas. We can also find this point practically using a compass, scale, and pencil.
Is the centroid always 2/3?
Yes, the centroid of a triangle will always be at a distance of 2/3 of the distance between a vertex and the midpoint of the sides
Is the centroid of a triangle 2/3 or 1/3?
The centroid of a triangle is at a distance of 2/3, not 1/3.
Where is the centroid of an acute triangle?
The centroid of an acute angle lies inside the figure. Doesn’t matter which type of triangle you are dealing with, the centroid point will be in its inside.
How do you find the centroid of a right triangle?
To find the centroid of a right triangle, we can use a specific formula or draw the medians. The point where all medians will meet is called the centroid of that triangle.
What are the Properties of the Centroid of a triangle?
The centroid of a triangle has specific properties given below:

It lies inside the figure.

There is only one centroid of one triangle.

The centroid of a triangle lies at a distance of 2/3 of the total distance between a vertex and a midpoint of the sides.
What is the Relationship Between the Orthocentre, Circumcentre, and Centroid of the Triangle?
In a triangle, the orthocenter, circumcenter, and centroid will be collinear. It means all these points lie on the same line