Centroid Formula
The geometric center of the object is known as the centroid. For determining the coordinates of the triangle’s centroid we use the centroid formula. The centroid of a triangle can be determined as the point of intersection of all the three medians of a triangle. The centroid of a triangle divides all the medians in a 2:1 ratio. Let us learn about the centroid formula with few solved examples at the end.
What is a Centroid Formula?
The centroid of a triangle is the center of the triangle. It is referred to as the point of concurrency of medians of a triangle. The centroid formula of a given triangle can be expressed as,
C = \( \left(\dfrac{x_1+ x_2+ x_3}{3} , \dfrac{y_1+ y_2+ y_3}{3}\right)\)
where,
 C denotes the centroid of a triangle
 \(x_1, x_2, x_3\) are the xcoordinates of the 3 vertices.
 \(y_1, y_2, y_3\) are the ycoordinates of the 3 vertices.
Let us have a look at a few solved examples to understand the centroid formula better.

Example 1: Vertices of the triangle are (4,3), (6,5), and (5,4). Determine the centroid of a triangle using the centroid formula.
Solution:
To find: Centroid of a triangle.
Given parameters are,
\((x_1, y_1) = (4,3)\)
\((x_2, y_2) = (6,5)\)
\((x_3, y_3) = (5,4)\)
Using centroid formula,
The centroid of a triangle = \(\dfrac{x_1, x_2, x_3}{3} , \dfrac{y_1, y_2, y_3}{3}\)
= \(\dfrac{4, 6, 5}{3} , \dfrac{3, 5, 4}{3}\)
= \(\dfrac{15}{3} , \dfrac{12}{3}\)
= (5 , 4)
Answer: The centroid of a triangle is (5 , 4).

Example 2: If the coordinates of the centroid of a triangle are (3, 3) and the vertices of the triangle are (1, 5), (1, 1), and (k, 3), then find the value of k.
Solution:
To find: The value of k
Given parameters are,
The centroid of a triangle is (3, 3)
\((x_1, y_1) = (1, 5)\)
\((x_2, y_2) = (1, 1)\)
\((x_3, y_3) = (k, 3)\)
Using the centroid formula,
The centroid of a triangle = \(\dfrac{x_1+ x_2+ x_3}{3} , \dfrac{y_1+ y_2+ y_3}{3}\)
(3, 3) = \(\dfrac{1+(1)+ k}{3} , \dfrac{5+1+3}{3}\)
(3, 3) = \(\dfrac{k}{3} , \dfrac{9}{3}\)
Equating the xcoordinates,
\(\dfrac{k}{3} = 3\)
k = 9
Answer: The value of k is 9.