- English

×

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

ADVERTISEMENT

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.

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.

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.

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

**Centroid = X _{1} + X_{2} + X_{3} / 3 , Y_{1} + Y_{2 }+ Y_{3 }/ 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.

*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.

X_{1} = 1 , Y_{1} = 2

X_{2} = 2 , Y_{2} = 3

X_{3} = 3 , Y_{3} = 1

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

= X_{1} + X_{2} + X_{3} , Y_{1} + Y_{2} + Y_{3}

= 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.

ADVERTISEMENT

X