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

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 #(2, 7 )#, #(1,5 )#, and #(7 , 5 )#?

1697 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-13T15:57:26

The centroid is

#= 3 , (19)/3#

The coordinates provided are
#(1,3) = color(blue)(x_1,y_1#
#(6,9) = color(blue)(x_2,y_2#
#(2,7) = color(blue)(x_3,y_3#

The formula required to find the centroid is as follows

centroid #=color(blue)[ (x_1+x_2+x_3)/3 , (y_1+y_2+y_3)/3]#

#= (1+6+2)/3 , (3 +9+7)/3#

#= (9)/3 , (19)/3#