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Centroid of a Triangle Calculator

Input the three vertices of a triangle in the centroid of a triangle calculator to find the centroid.

Formula:
M = x1+x2+x33 , y1+y2+y33

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This online calculator finds the centroid of a triangle in 2 dimensions. It means you can compute the center point of the triangle known as a centroid.

What is a Centroid?

A centroid is a point where the three medians of a triangle bisect each other. If a polygon is fixed at its centroid, the figure becomes geometrically balanced. 

centroid of triangle

A very common mistake people make is that they think the centroid divides medians in half. Actually, the centroid is the point that divides medians in the ratio of 2:1.

Centroid of a Triangle Formula

The formulas of the centroid are different for polygons. The formula used to compute the centroid of a triangle is:

Centroid = X1 + X2 + X3 / 3 , Y1 + Y2 + Y3 / 3

It is very similar to the formula of the midpoint. It is important to note that the answer is in the form of a point.

How to calculate the Centroid of a Triangle?

Example:

The points A, B, and C of a triangle are (1,2), (2,3), and (3,1) respectively. Find the centroid of this triangle.

Solution: 

Step 1: Write all the vertices. 

X1 = 1 , Y1 = 2 

X2 = 2 , Y2 = 3

X3 = 3 , Y3 = 1

Step 2: Add all the X vertices and Y vertices.

= X1 + X2 + X3 , Y1 + Y2 + Y3 

= 1 + 2 + 3 , 3 + 2 + 1

= 6 , 6

Step 3: Divide both sums by 3.

= 6/3 , 6/3

= 2 , 2 

Hence, the centroid of this triangle exists on point (2,2) on the cartesian plane. 

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