A triangle has corners at #(1 ,9 )#, #(5 ,4 )#, and #(6 ,8 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2017-05-08T12:55:18

The distance is #=8.06#

Let #ABC# be the triangle

#A=(1,9)#

#B=(5,4)#

#C=(6,8)#

The centroid of triangle #ABC# is

#C_c=((1+5+6)/3,(9+4+8)/3)=(12/3,21/3)=(4,7)#

The distance of the centroid from the origin is

#=sqrt(4^2+7^2)#

#=sqrt(16+49)#

#=sqrt65#

#=8.06#