A triangle has corners at (6 ,6 ), (7 ,4 ), and (5 ,2 ). How far is the triangle's centroid from the origin?

1 Answer
Jun 26, 2016

sqrt 52

Explanation:

Centroid Formula is

C = ((x_1+x_2+x_3)/3, (y_1+y_2+y_3)/3) where

x_1, x_2, x_3 are the x-coordinates of the vertices of the triangle.
y_1, y_2, y_3 are the y-coordinate’s of the vertices of the triangle.

In our triangle,

(x_1, y_1) = (6,6)

(x_2,y_2) = (7,4)

(x_3,y_3) = (5,2)

The centroid coordinates are

C = ((6+7+5)/3, (6+4+2)/3) => (18/3, 12/3) => (6,4)

Distance from origin (0,0) to C(6,4) using the distance formula is

D = sqrt(6^2+4^2)

=sqrt (36+16)

= sqrt 52