A triangle has corners at #(9 ,1 )#, #(2 ,7 )#, and #(5 ,8 )#. How far is the triangle's centroid from the origin?

1 Answer
jags
Jul 3, 2016

#=16/3sqrt (2)#

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) = (9,1)#

#(x_2,y_2) = (2,7)#

#(x_3,y_3) = (5,8)#

The centroid coordinates are

#C = ((9+2+5)/3, (1+7+8)/3) => (16/3, 16/3)#

Distance from origin #(0,0)# to #C(16/3, 16/3)# using the distance formula is

#D = sqrt((16/3)^2+(16/3)^2)#

#=16/3sqrt (2)#

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