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

1 Answer
jags · Stefan V.
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#

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