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Solution
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Solution provided by AtoZmath.com
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Centroid of a triangle calculator
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 1. Find the centroid of a triangle whose vertices are `A(4,-6),B(3,-2),C(5,2)`
2. Find the centroid of a triangle whose vertices are `A(3,-5),B(-7,4),C(10,-2)`
3. Find the centroid of a triangle whose vertices are `A(4,-8),B(-9,7),C(8,13)`
4. Find the centroid of a triangle whose vertices are `A(3,-7),B(-8,6),C(5,10)`
5. Find the centroid of a triangle whose vertices are `A(2,4),B(6,4),C(2,0)`
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Example1. Find the centroid of a triangle whose vertices are `A(4,-6),B(3,-2),C(5,2)`Solution:If `A(x_1,y_1),B(x_2,y_2)` and `C(x_3,y_3)` are the three vertices of the triangle ABC,
then the centroid of the triangle ABC is given by `G(x,y)=((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)` The given points are `A(4,-6),B(3,-2),C(5,2)` `:. x_1=4,y_1=-6,x_2=3,y_2=-2,x_3=5,y_3=2` Let `G(x,y)` be the centroid of the triangle ABC `:. x=(x_1+x_2+x_3)/3` `=(4+3+5)/3` `=12/3` `=4` `:. y=(y_1+y_2+y_3)/3` `=(-6-2+2)/3` `=-6/3` `=-2` `:.` Centroid of triangle ABC is `G(4,-2)` 
2. Find the centroid of a triangle whose vertices are `A(3,-5),B(-7,4),C(10,-2)`Solution:If `A(x_1,y_1),B(x_2,y_2)` and `C(x_3,y_3)` are the three vertices of the triangle ABC,
then the centroid of the triangle ABC is given by `G(x,y)=((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)` The given points are `A(3,-5),B(-7,4),C(10,-2)` `:. x_1=3,y_1=-5,x_2=-7,y_2=4,x_3=10,y_3=-2` Let `G(x,y)` be the centroid of the triangle ABC `:. x=(x_1+x_2+x_3)/3` `=(3-7+10)/3` `=6/3` `=2` `:. y=(y_1+y_2+y_3)/3` `=(-5+4-2)/3` `=-3/3` `=-1` `:.` Centroid of triangle ABC is `G(2,-1)` 
3. Find the centroid of a triangle whose vertices are `A(4,-8),B(-9,7),C(8,13)`Solution:If `A(x_1,y_1),B(x_2,y_2)` and `C(x_3,y_3)` are the three vertices of the triangle ABC,
then the centroid of the triangle ABC is given by `G(x,y)=((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)` The given points are `A(4,-8),B(-9,7),C(8,13)` `:. x_1=4,y_1=-8,x_2=-9,y_2=7,x_3=8,y_3=13` Let `G(x,y)` be the centroid of the triangle ABC `:. x=(x_1+x_2+x_3)/3` `=(4-9+8)/3` `=3/3` `=1` `:. y=(y_1+y_2+y_3)/3` `=(-8+7+13)/3` `=12/3` `=4` `:.` Centroid of triangle ABC is `G(1,4)` 
4. Find the centroid of a triangle whose vertices are `A(3,-7),B(-8,6),C(5,10)`Solution:If `A(x_1,y_1),B(x_2,y_2)` and `C(x_3,y_3)` are the three vertices of the triangle ABC,
then the centroid of the triangle ABC is given by `G(x,y)=((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)` The given points are `A(3,-7),B(-8,6),C(5,10)` `:. x_1=3,y_1=-7,x_2=-8,y_2=6,x_3=5,y_3=10` Let `G(x,y)` be the centroid of the triangle ABC `:. x=(x_1+x_2+x_3)/3` `=(3-8+5)/3` `=0/3` `=0` `:. y=(y_1+y_2+y_3)/3` `=(-7+6+10)/3` `=9/3` `=3` `:.` Centroid of triangle ABC is `G(0,3)` 
5. Find the centroid of a triangle whose vertices are `A(2,4),B(6,4),C(2,0)`Solution:If `A(x_1,y_1),B(x_2,y_2)` and `C(x_3,y_3)` are the three vertices of the triangle ABC,
then the centroid of the triangle ABC is given by `G(x,y)=((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)` The given points are `A(2,4),B(6,4),C(2,0)` `:. x_1=2,y_1=4,x_2=6,y_2=4,x_3=2,y_3=0` Let `G(x,y)` be the centroid of the triangle ABC `:. x=(x_1+x_2+x_3)/3` `=(2+6+2)/3` `=10/3` `:. y=(y_1+y_2+y_3)/3` `=(4+4)/3` `=8/3` `:.` Centroid of triangle ABC is `G(10/3,8/3)` 
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