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# Centroid Formula

The Centroid of a Triangle is the centre of the triangle that can be calculated as the point of intersection of all the three medians of a triangle. The median is a line drawn from the midpoint of a side to the opposite vertex. The centroid separates all the medians of the triangle in the ratio 2:1.

The Centroid Formula is,

Where,
C is the centroid of the triangle.
x1,x2,x3 are the x-coordinate’s of the vertices of the triangle.
y1,y2,y3 are the y-coordinate’s of the vertices of the triangle.

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## Centroid Problems

Some solved problems on centroid are given below:

### Solved Examples

Question 1: Find the centroid of a triangle whose vertices are (5,3), (6,1) and (7,8) ?
Solution:

Given,
(x1,y1) = (5,3)
(x2,y2) = (6,1)
(x3,y3) = (7,8)

The centroid formula is,
C = ($\frac{x_{1}+x_{2}+x_{3}}{3}$,$\frac{y_{1}+y_{2}+y_{3}}{3}$)

C = ($\frac{5+6+7}{3}$,$\frac{3+1+8}{3}$)

C = ($\frac{18}{3}$,$\frac{12}{3}$)

C = (6,4)

Question 2: Find the centroid of a triangle whose vertices are (9,0), (2,8) and (1,4) ?
Solution:

Given,
(x1,y1) = (9,0)
(x2,y2) = (2,8)
(x3,y3) = (1,4)

The centroid formula is,
C = ($\frac{x_{1}+x_{2}+x_{3}}{3}$,$\frac{y_{1}+y_{2}+y_{3}}{3}$)

C = ($\frac{9+2+1}{3}$,$\frac{0+8+4}{3}$)

C = ($\frac{12}{3}$,$\frac{12}{3}$)

C = (4,4)

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