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

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 )#?

1804 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-10T00:43:18

The centroid is located at #(17/3,8/3)#.

The centroid of a triangle is the intersection of the medians and is found with this formula:

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

where #(x_1, y_1)#, #(x_2,y_2)# and #(x_3,y_3)# are the vertices of the triangle.

In this example, the vertices are #(9,5), (6,0), (2,3)#

The centroid is

#((9+6+2)/3, (5+0+3)/3)= (17/3, 8/3)#