Centroid Calculator
Centroid Calculator is a free handy online tool that determines the centroid of a triangle in just few seconds. Simply, enter the input coordinates in the below boxes and hit on the calculate button to check the output in a blink of eye.
Centroid Calculator: Looking to learn concept centroid of a triangle? You are at the correct place. Here, we have given the detailed steps to find the centroid of a triangle along with the formula to find it. If you want to know more about the topic then please go with this article and take help from our handy Centroid Calculator. This tool does your calculations much easier and displays the work along with the output at a faster peace.
How to Find Centroid of a Triangle?
In order to calculate the centroid of a triangle, go through the simple steps provided below
- Take the three vertices of any type of triangle.
- Find the mean of x coordinates and y coordinates.
- Add all vertices x coordinates and y coordinates.
- Divide the obtained number by 3 to get the result.
Centroid Formula
Centroid is nothing but the Centre point of any object. Centroid of a triangle is defined as the point where three medians of a triangle intersect. Median is a line that joins the midpoint of the side and opposite vertex of the triangle. The formula to find the centroid of a triangle ABC is
Centroid = ((x₁ + x₂ + x₃) / 3, (y₁ + y₂ + y₃)/3)
Where
(x₁, y₁) coordinates of A
(x₂, y₂) coordinates of B
(x₃, y₃) coordinates of C
For special triangles, centroid is defines as follows
Equilateral Triangle
Centroid = (a/2, a√3/6), a is the side of triangle.
Isosceles Triangle
Centroid = (l/2, h/3), l is the length and h is the height of triangle.
Right Angled Triangle
Centroid = (b/3, h/3), b is the base and h is the height of triangle.
Example
Question: Determine the centroid of a triangle whose vertices are (5,3), (6,1) and (7,8)?
Solution:
Given vertices are
(x₁, y₁) = (5,3)
(x₂, y₂) = (6,1)
(x₃, y₃) = (7,8)
Centroid formula is given by
Centroid = ((x₁ + x₂ + x₃) / 3, (y₁ + y₂ + y₃)/3)
= ((5 + 6 + 7) / 3, (3 + 1 + 8) / 3)
= (18 / 3, 12 / 3)
= (6, 4)
Centroid for the given vertices is (6, 4).
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Frequently Asked Questions on Centroid Calculator
1. What are the properties of centroid of a triangle?
Centroid is always located in the interior of the triangle. It is located 2/3 of the distance from the vertex along the segment that connects vertex to the midpoint of the opposite side.
2. What is meant by Triangle Centroid?
Every triangle has exactly three medians, one from each vertex. All those medians intersect each other at point point. That point is called triangle centroid.
3. What is the formula of centroid of triangle?
Centroid = ((x₁ + x₂ + x₃) / 3, (y₁ + y₂ + y₃)/3) Where (x₁, y₁), (x₂, y₂), (x₃, y₃) are coordinates of triangle.
4. Find the centroid of the triangle whose vertices are: (3,-5),(-7,4),(10,-2)?
G = (x, y) = [(x₁ + x₂ + x₃) / 3, (y₁ + y₂ + y₃)/3]
= [(3 - 7 + 10) / 3, (-5 + 4 - 2) / 3]
= [6 / 3, -3 / 3]
=(2, -1)