A triangle has corners at #(4 ,3 )#, #(2 ,6 )#, and #(1 ,5 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2017-06-28T11:28:49

The distance is #=5.2#

The centroid of the triangle, #A=(4,3)#, #B=(2,6)# and #C=(1,5)# is

#C_c=((x_A+x_B+x_C)/3,(y_A+y_B+y_C)/3)=((4+2+1)/3,(3+6+5)/3)#

#=(7/3,14/3)#

The distance of the centroid from the origin is

#=sqrt((7/3)^2+(14/3)^2)#

#=sqrt(49/9+196/9)#

#=sqrt(245)/3#

#=5.2#