Centroid Formula

 

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.

Centroid Formula
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)

 

 


Practise This Question

The sides of ΔABC are 6cm, 8cm and 10cm. Find the perimeter of the larger triangle which is similar to ΔABC if the ratio of corresponding sides is 2.