A triangle has corners at #(1 ,4 )#, #(3 ,5 )#, and #(3 ,2 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2017-03-21T08:16:48

The distance is #=4.35#

Let #ABC# be the triangle

#A=(1,4)#

#B=(3,5)#

#C=(3,2)#

The centroid of triangle #ABC# is

#C_c=((1+3+3)/3,(4+5+2)/3)=(7/3,11/3)#

The distance of the centroid from the origin is

#=sqrt((7/3-0)^2+(11/3-0)^2)#

#=sqrt(49/9+121/9)#

#=1/3sqrt170#

#=4.35#