A triangle has corners at #(5 ,6 )#, #(3 ,2 )#, and #(8 ,9 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2016-11-26T08:17:02

The distance is #=sqrt545/3=7.8#

Let the vertices of a triangle be #(x_1,y_1)#, #(x_2,y_2)# and
#(x_3,y_3)#

Then the centroid is #(x_c, y_c)#

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

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

And the distance of the centroid from the origin is

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

Here we have, #(5,6)#, #(3,2)# and #(8,9)#

#x_c=(5+3+8)/3=16/3#

#y_c=(6+2+9)/3=17/3#

#d=sqrt(16^2/3^2+17^2/3^2)#

#=(sqrt545)/3=7.8#