A triangle has corners at #(1 ,9 )#, #(5 ,4 )#, and #(6 ,2 )#. How far is the triangle's centroid from the origin?

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A triangle has corners at #(1 ,9 )#, #(5 ,4 )#, and #(6 ,2 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2018-05-05T03:33:17

#sqrt41# units

Explanation:

A triangle with vertices at #(x_1,y_1), (x_2,y_2) and (x_3,y_3)# has centroid at #((x_1+x_2+x_3)/3, (y_1+y_2+y_3)/3)#
#=># centroid of the triangle #=((1+5+6)/3, (9+4+2)/3)=(4,5)#
Let #d# be the distance between the centroid and the origin #O(0,0)#,
#=> d=sqrt(4^2+5^2)=sqrt(16+25)=sqrt41# units

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A triangle has corners at #(1 ,9 )#, #(5 ,4 )#, and #(6 ,2 )#. How far is the triangle's centroid from the origin?

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