A triangle has corners at #(7 ,2 )#, #(6 ,7 )#, and #(3 ,1 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2017-07-23T14:53:27

The distance is #=6.3#

The centroid is

#(x_c,y_c)=((x_1+x_1+x_3)/3,(y_1+y_2+y_3)/3)#

Therefore,

#(x_c,y_c)=((7+6+3)/3,(2+7+1)/3)=(16/3,10/3)#

The distance from the origin is

#d_C=sqrt((x_c)^2+(y_c)^2)#

#=sqrt((16/3)^2+(10/3)^2)#

#=sqrt356/3#

#=6.3#