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Centroid Triangle

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Centroids are the most important features of triangles; also, they have applications to aeronautics as they relate to the center of gravity (CG) of shapes. Well, come to the point, at this platform, we are provided a centroid of a triangle calculator that allows you to find coordinates on the centroid of triangle for given coordinates of the 3-vertices.

Before knowing about this centroid calculator for triangle centroid, let’s take a look!

The point through which all the three medians of a triangle pass is said to be as the centroid of a triangle. More specifically, if you draw lines from each corner (or vertex) of a triangle t the midpoint of the opposite sides, then those three lines meet at a center or centroid of the triangle. It is also said to be ‘center of gravity of triangle’ where the triangle balances evenly, ‘center of mass of a triangle, or barycenter.’ Keep in mind; centroid has several numbers of properties and relations with other parts of the triangle that includes its circumcenter, incenter, orthocenter, area, and much more!

Simply, the coordinates of the centroid are the average of the coordinates of the vertices. So, if you want to find the x coordinates of the orthocenter, then you ought to add up the three vertex x coordinates and divide by 3: repeat, the same for the y coordinate.

**The centroid of a triangle formula is:**

According to centroid theorem, the centroid equation is stated as:

{(x1+x2+x3)/3, (y1+y2+y3)/3}

The first thing that you have to remember that centroid is the center point equidistant from all vertices.

Now let’s start with the formula:

Ox = x1+x2+x3/3

Oy = y1+y2+y3/3

**For example:**

Suppose that abc triangle has vertices A = (4,5), B = (20,25), and C = (30,6). How to find coordinates of the centroid?

**Solution:**

- First of all, you have to identify the coordinates of each vertex in the triangle, in the above example, the vertices are A = (4,5), B = (20,25), and C = (30,6).
- Very next, you have to add all the x values from the three vertices coordinates and divide by 3 to get the x value of the centroid coordinate.

Ox = 4 + 20 + 30 / 3

Ox = 54 / 3

Ox = 18

- Then, you have to add all the y values from the three vertices coordinates and divide by 3 to get the y value of the centroid coordinate.

Oy = 5 + 25 + 6 / 3

Oy = 36 / 3

Oy = 12

- Finally, you determined the centroid coordinate from the above calculations, centroid coordinate = (18, 12)

So, you can draw this centroid into the triangle to illustrate its center position.

Yes, this highly accurate centroid of a triangle calculator through which you can readily calculate centroid of the triangle ABC. This centroid calculator will work efficiently to find centroid of any triangle when the vertices are known. Sometimes, this tool is referring as a center of mass calculator, geometric center, or barycenter calculator.

The tool is specifically designed with user-friendly that determines the centroid of a right triangle or any triangle when the vertices are given. Let’s take a look!

- You just have to enter the x,y coordinates of each vertex, in any order into the designated field of the above calculator
- Once done, hit the calculate button, the calculator shows the coordinates of the centroid or center of the triangle

The centroid of an equilateral triangle can readily find as it is always located inside the triangle like the (incenter, another one the triangle’s concurrent points). Remember that the centroid divides each median in a ratio of 2:1. More specifically, the centroid will always be 2/3 of the way with any given median towards the vertex, and 1/3 towards the side.

The point where all three altitudes of the triangle intersect is said to be as the orthocenter of a triangle. A line that passes through a vertex of the triangle and perpendicular to the opposite side is known as altitude. Thus, there are three altitudes in a triangle.

- The intersection of the medians always forms centroid
- It is said to be as one of the points of concurrency of a triangle
- It is always located inside the triangle
- Centroid divides each median in a ratio of 2:1. In other words, it will always be 2/3 of the way along any given median

By definition, the centroid is said to be a point of a concurrency of the triangle. It represents the point where all 3 medians intersect and are typically described as the barycent or the triangle’s center of gravity. It always formed by the intersection of the medians.

Get the ease with the above centroid of a triangle calculator, formula, and solved example to understand, practice, and verify such geometrical calculations. Unlike most of the other online calculators, it provides you with the tested step by step calculations!