What is the centroid of a triangle with corners at #(2, 7 )#, #(1,5 )#, and #(7 , 5 )#?

Question

What is the centroid of a triangle with corners at #(5, 1)#, #(4, 9)#, and #(7,2)#?
What is the centroid of a triangle with corners at #(5, 2 )#, #(2, 5)#, and #(7,2)#?
What is the centroid of a triangle with corners at #(5, 2 )#, #(2, 5 )#, and #(5,3 )#?
What is the centroid of a triangle with corners at #(1, 4 )#, #(3, 5 )#, and #(5,3 )#?
What is the centroid of a triangle with corners at #(1, 1 )#, #(3, 2 )#, and #(8 , 6 )#?
What is the centroid of a triangle with corners at #(6, 1 )#, #(2, 2 )#, and #(1 , 6 )#?
What is the centroid of a triangle with corners at #(3, 1 )#, #(5, 2 )#, and #(12 , 6 )#?
What is the centroid of a triangle with corners at #(3, 2 )#, #(5,5 )#, and #(12 , 9 )#?
What is the centroid of a triangle with corners at #(3, 2 )#, #(1,5 )#, and #(0 , 9 )#?
What is the centroid of a triangle with corners at #(4, 7 )#, #(1,2 )#, and #(8 , 5 )#?

2229 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-10T10:00:55

Centroid is #(10/3,17/3)#

For triangle with vertices #(x_1,y_1), (x_2,y_2)# and #(x_3,y_3)#
The centroid #G(x,y)# where formula to find #x# and #y# is given by

#x=(x_1+x_2+x_3)/3# and #y=(y_1+y_2+y_3)/3#

Now let us apply this to our problem.

Vertices are given as #(2,7),(1,5)# and #(7,5)#

#x_1=2, y_1=7#

#x_2=1, y_2=5#

#x_3=7,y_3=5#

#x=(2+1+7)/3# and #y=(7+5+5)/3#
#x=10/3# and #y=17/3#

Centroid #G(x,y) = (10/3,17/3)#