Centroid Formula

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. The centroid divides all the medians of the triangle in 2:1 ratio.

The Centroid Formula is given by

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

Where in,

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.

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)