A triangle has corners at #(1 ,9 )#, #(5 ,4 )#, and #(3 ,8 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2016-06-18T15:41:52

It is #7.61#.

If #(A_x, A_y), (B_x, B_y), (C_x, C_y)# are the vertex of a triangle, the coordinates of the centroid are

#CO_x=(A_x+B_x+C+x)/3#

#CO_y=(A_y+B_y+C+y)/3#

In our case

#CO_x=(1+5+3)/3=9/3=3#

#CO_y=(9+4+8)/3=21/3=7#

Then the centroid has coordinates #(3, 7)# and its distance from the origin is simply

#d=sqrt(3^2+7^2)=sqrt(9+49)=sqrt(58)\approx7.61#.

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