A triangle has corners at #(5 ,2 )#, #(2 ,7 )#, and #(3 ,5 )#. How far is the triangle's centroid from the origin?

1 Answer
Shwetank Mauria
Apr 30, 2016

The triangle's centroid is #5.735# units from the origin.

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 #(5,2)#, #(2,7)# and #(3,5)#, the centroid of given triangle is #((5+2+3)/3,(2+7+5)/3)# or #(10/3,14/3)#.

And its distance from origin is #sqrt((10/3-0)^2+(14/3-0)^2)=sqrt(100/9+196/9)=sqrt(296/9)#

= #1/3sqrt2xx2xx74=2/3xxsqrt74=2/3xx8.602=5.735#

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