A triangle has corners at #(7 ,6 )#, #(4 ,3 )#, and #(5 ,7 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2017-05-19T05:38:10

The distance is #=7.54#

Let #ABC# be the triangle

#A=(7,6)#

#B=(4,3)#

#C=(5,7)#

The centroid of triangle #ABC# is

#C_c=((7+4+5)/3,(6+3+7)/3)=(16/3,16/3)#

The distance of the centroid from the origin is

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

#=16/3sqrt(2)#

#=7.54#