 # Centroid Formula

Centroid formula is used to determine the coordinates of a triangle’s centroid. The centroid of a triangle is the center of the triangle which can be determined as the point of intersection of all the three medians of a triangle. The median is a line drawn from the midpoint of any one side to the opposite vertex. It should be noted that the centroid divides all the medians of the triangle in 2:1 ratio. ## Centroid Formula

The Centroid Formula is given by

 Formula for Centroid C = (x1 + x2 + x3 / 3, y1 + y2 + y3 / 3)

Where,

• C denotes centroid of the triangle.
• x1, x2, x3 are the x-coordinates of the vertices of a triangle.
• y1, y2, y3 are the y-coordinates of the vertices of a triangle.

### Solved Example Questions From Centroid Formula

Example 1:

Determine the centroid of a triangle whose vertices are (5,3), (6,1) and (7,8).

Solution

Given parameters are,

(x1, y1) = (5,3)

(x2, y2) = (6,1)

(x3, y3) = (7,8)

The centroid formula is given by

C = (x1 + x2 + x3 / 3 , y1 + y2 + y3 / 3)

C = (5 + 6 + 7 / 3 , 3 + 1 + 8 / 3

C = (18 / 3 , 12 / 3)

C = (6, 4)

Example 2:

Calculate the centroid of a triangle whose vertices are (9,0), (2,8) and (1,4).

Solution

Given parameters are

(x1, y1) = (9, 0)

(x2, y2) = (2, 8)

(x3, y3) = (1, 4)

The centroid formula is given by,

C = (x1 + x2 + x3 / 3 , y1 + y2 + y3 / 3)

C = (9 + 2 + 1 / 3 , 0 + 8 + 4 / 3)

C = (12 / 3 , 12 / 3)

C = (4, 4)