What is the centroid of a triangle with corners at #(3, 2 )#, #(5,5 )#, and #(12 , 9 )#?

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

2099 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-16T17:34:24

The centroid # = (20)/3 , (16)/3#

The corners of the triangle are
#(3,2) = color(blue)(x_1,y_1#
#(5,5) = color(blue)(x_2,y_2#
# (12,9) = color(blue)(x_3,y_3#

The centroid is found using formula

centroid # = (x_1+x_2+x_3)/3 , (y_1+y_2+y_3)/3#

# = (3+5+12)/3 , (2+5+9)/3#

# = (20)/3 , (16)/3#