1. Find the centroid of a triangle whose vertices are A(4,-6),B(3,-2),C(5,2)
1. 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)
This material is intended as a summary. Use your textbook for detail explanation.
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