A triangle has corners at #(9 ,3 )#, #(7 ,5 )#, and #(3 ,1 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2016-12-13T09:28:31

The answer is #=7#

If the corners of a triangle are #(x_1,y_1)#, #(x_2,y_2)# and #(x_3,y_3)#

The centroid is #((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)#

Therefore,

we have #x_g=(9+7+3)/3=19/3#

and #y_g=(3+5+1)/3=3#

The distance of #(x_g,y_g)# from the origin is

#=sqrt(x_g^2+y_g^2)=sqrt(19^2/9+9)=7#