Centroid calculator calculates the intersection point of three medians of a triangle. It only takes all three coordinates of h and y and finds the centroid of the triangle in no time at all. In this post, we will discuss centroid definition, the centroid of a triangle formula, and how to find the 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.
The point at which all medians of a triangle intersects each other is called the centroid of a 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.
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.
You need to use mean vertex coordinates to find the center of the triangle ABC. The centroid formula for \(A = (X_1, Y_1), B = (X_2, Y_2), C = (X_3, Y_3)\) will be:
\(G = \Big[\dfrac{(X_1 + X_2 + X_3)}{3}, \dfrac{(Y_1 + Y_2 + Y_3)}{3}\Big]\)
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.
\(x_1= -1, x_2 = 2, x_3= 8\)
\(y_1= -3, y_2 = 1, y_3= -4\)
Step 3: Substitute all values in the centroid of a triangle equation.
\(G = \Big[\dfrac{(X_1 + X_2 + X_3)}{3}, \dfrac{(Y_1 + Y_2 + Y_3)}{3}\Big]\)
\(G = \Big(\dfrac{(-1 + 2 + 8)}{3}, \dfrac{(-3 + 1 - 4)}{3}\Big)\)
\(G = \Big( \dfrac{9}{3} , \dfrac{-6}{3}\Big)\)
\(G = (3, -2)\)
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.
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