A triangle has corners at #(2 ,9 )#, #(7 ,8 )#, and #(4 ,3 )#. How far is the triangle's centroid from the origin?

1 Answer
Shwetank Mauria
Apr 30, 2016

The triangle's centroid is #7.951# 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 #(2,9)#, #(7,8)# and #(4,3)#, the centroid of given triangle is #((2+7+4)/3,(9+8+3)/3)# or #(13/3,20/3)#.

And its distance from origin is #sqrt((13/3-0)^2+(20/3-0)^2)=sqrt(169/9+400/9)=sqrt(569/9)#

= #1/3sqrt569=1/3xxsqrt74=1/3xx23.854=7.951#

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