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

Where,

C is the centroid of the triangle.

x

y

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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,

(x_{1},y_{1}) = (5,3)

(x_{2},y_{2}) = (6,1)

(x_{3},y_{3}) = (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,

(x_{1},y_{1}) = (9,0)

(x_{2},y_{2}) = (2,8)

(x_{3},y_{3}) = (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)

Given,

(x

(x

(x

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)

Given,

(x

(x

(x

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)