A triangle has corners at #(1 ,9 )#, #(3 ,4 )#, and #(4 ,2 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2017-02-03T19:01:35

The answer is #=5.7#

The centroid#(x_c,y_c)# of a triangle with corners #(x_1,y_1)#, #(x_2,y_2)# and #(x_3,y_3)# is

#x_c=(x_1+x_2+x_3)/3#

#y_c=(y_1+y_2+y_3)/3#

Therefore,

#x_c=(1+3+4)/3=8/3#

#y_c=(9+4+2)/3=15/3=5#

The distance from the origin is

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

#=sqrt(8^2/9+5^2)#

#=sqrt(64/9+25)#

#=sqrt289/3=5.7#