A triangle has corners at #(4 ,1 )#, #(6 ,3 )#, and #(3 ,8 )#. How far is the triangle's centroid from the origin?

1 Answer
Shwetank Mauria
Apr 29, 2016

Distance of centroid from origin is #5.897#

Explanation:

Coordinates of centroid of a triangle whose vertices (corners) are #(x_1,y_1)#, #(x_2,y_2)# and #(x_3,y_3)# is given by

#((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)#

As corners of triangle are #(4,1)#, #(6,3)# and #(3,8)#, the centroid of given triangle is #((4+6+3)/3,(1+3+8)/3)# or #(13/3,4)#.

And its distance from origin is #sqrt((13/3-0)^2+(4-0)^2)=sqrt(169/9+16)=sqrt(169/9+144/9)#

= #sqrt((169+144)/9)=sqrt(313/9)=1/3sqrt313=1/3xx17.692=5.897#

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