What is the centroid of a triangle with corners at #(5 , 7 )#, #(3 , 5 )#, and #(6 , 2 )#?

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 )#?

1512 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-16T17:25:01

The centroid #=(14/3 , 14/3)#

The coordinates of the vertices of the triangle are

#(5,7) = color(blue)(x_1,y_1#

#(3,5) = color(blue)(x_2,y_2#

#(6,2) = 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#

#=(5+3+6)/3 , (7+5+2)/3#

#=14/3 , 14/3#