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

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Answer 1 · 2017-01-27T15:42:51

The distance is #=6.9#

If we have a triangle has corners #(x_1,y_1)# ; #(x_2, y_2)# and #(x_3,y_3)#

The coordinates of the centroid are

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

and

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

and the distance from the orogin is

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

Here, we have

#x_c=(4+8+5)/3=17/3#

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

Therefore,

#OC=sqrt((17/3)^2+(4^2))=sqrt48.11=6.9#