A triangle has corners at #(2 ,9 )#, #(4 ,8 )#, and #(5 ,1 )#. How far is the triangle's centroid from the origin?

1 Answer
Shwetank Mauria
Apr 29, 2016

Distance of centroid from origin is #7.032#

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 #(2,9)#, #(4,8)# and #(5,1)#, the centroid of given triangle is #((2+4+5)/3,(9+8+1)/3)# or #(11/3,6)#.

And its distance from origin is #sqrt((11/3-0)^2+(6-0)^2)=sqrt(121/9+36)=sqrt(121/9+324/9)#

= #sqrt((121+324)/9)=sqrt(445/9)=1/3sqrt445=1/3xx21.095=7.032#

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