A triangle has corners at #(9 ,3 )#, #(7 ,4 )#, and #(3 ,1 )#. How far is the triangle's centroid from the origin?

2 Answers
Shwetank Mauria
May 25, 2016

Triangle's centroid from the origin is #6.872# units away.

Explanation:

Centroid of a triangle, whose corners are #(x_1,y_1)#, #(x_2,y_2)# and #(x_3,y_3)#, is given by #(1/3(x_1+x_2+x_3),1/3(y_1+y_2+y_3))#

Hence centroid of the triangle whose corners are #(9,3)#, #(7.4)# and #(3,1)# is

#(1/3(9+7+3),1/3(3+4+1))# or #(19/3,8/3)#

And its distance from origin #(0,0)# is

#sqrt((19/3-0)^2+(8/3-0)^2)=sqrt(361/9+64/9)#

= #1/3sqrt425=1/3xx20.616=6.872#

Shwetank Mauria
May 25, 2016

Triangle's centroid is #6.872# units away from the origin.

Explanation:

Centroid of a triangle, whose corners are #(x_1,y_1)#, #(x_2,y_2)# and #(x_3,y_3)#, is given by #(1/3(x_1+x_2+x_3),1/3(y_1+y_2+y_3))#

Hence centroid of the triangle whose corners are #(9,3)#, #(7.4)# and #(3,1)# is

#(1/3(9+7+3),1/3(3+4+1))# or #(19/3,8/3)#

And its distance from origin #(0,0)# is

#sqrt((19/3-0)^2+(8/3-0)^2)=sqrt(361/9+64/9)#

= #1/3sqrt425=1/3xx20.616=6.872#

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