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Centroid calculator is an online tool that can be used to calculate the centroid of a triangle. In other words, it calculates the intersection point of three medians of a triangle. It only takes all three coordinates of h and y from the user and finds the centroid of the triangle in no time at all. Now you don’t have to worry about complex triangles and their centroid calculation.
In this post, we will discuss centroid definition, centroid of a triangle formula, how to find centroid, and much more.
How to use Centroid Triangle Calculator?
If you want to calculate the centroid of a right triangle or centroid of a trapezoid, this calculator is the best tool you will come across. It is developed to simplify the centroid calculations. To use this calculator, follow the steps below:
- Enter coordinates for x1 and y1
- Enter coordinates for x2 and y2
- Enter coordinates for x3 and y3
- Press the Calculate button to get the coordinates of the centroid.
It will give you the step by step calculation and substitution so that you can understand the whole process of calculation. This is the best thing about our calculators: they are not just developed to solve the equations but to improve understanding and knowledge as well.
What is a Centroid?
The center of mass of an object with equal density is known as centroid. You can picture it as the point to place the tip of the pin in order to achieve that geometrical balance. It is also known as a geometric center.
Centroid formula
A centroid is usually the average of all the points in a triangle. The formula for centroid can be written as:
\(Gx = \dfrac{(x1 + x2 + x3 +... + xk)}{k}\)
\(Gy = \dfrac{(y1 + y2 + y3 +... + yk)}{k}\)
The centroid lies within the body for convex shapes; the centroid may lie outside for concave shapes. The formula of the centroid is comparatively simple. In the case of other shapes like rhombus or rectangle, the calculations could be much more complicated as compared to the triangle.
How to find the centroid of a triangle?
The point at which all medians of a triangle intersects each other is called the centroid of triangle. It is one of the points of concurrency of a triangle. In addition, each median is separated in a 2:1 relation by a centroid, and the bigger segment is closer to the vertex.
You need to use mean vertex coordinates to find the center of the triangle ABC. The centroid formula for \(A = (X1, Y1), B = (X2, Y2), C = (X3, Y3)\) will be:
\(G = \Big[\dfrac{(X1 + X2 + X3)}{3}, \dfrac{(Y1 + Y2 + Y3)}{3}\Big]\)
Example:
If vertices of a triangle are \((-1, -3), (2, 1)\) and \((8, -4)\), find the centroid of the triangle.
Solution:
Follow these steps to find the centroid of a triangle using the given vertices of that triangle.
Step 1: Identify the vertices of the triangle.
\((-1, -3), (2, 1), (8, -4)\)
Step 2: Identify x and y coordinates.
\(x1= -1, x2 = 2, x3= 8\)
\(y1= -3, y2 = 1, y3= -4\)
Step 3: Substitute all values in the centroid of a triangle formula.
\(G = \Big[\dfrac{(X1 + X2 + X3)}{3}, \dfrac{(Y1 + Y2 + Y3)}{3}\Big]\)
\(G = \Big(\dfrac{(-1 + 2 + 8)}{3}, \dfrac{(-3 + 1 - 4)}{3}\Big)\)
\(G = \Big( \dfrac{9}{3} , \dfrac{-6}{3}\Big)\)
\(G = (3, -2)\)
So, the centroid of a triangle with the vertices \((-1, -3), (2, 1)\) and \((8, -4)\) will be \((3, -2)\). You can always use our centroid calculator if you don’t want to do it manually.