A triangle has corners at #(5 ,1 )#, #(7 ,2 )#, and #(6 ,7 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2016-11-13T00:32:07

The distance between the centroid and the origin is #d=2/3 sqrt106#

The centroid of a triangle can be found by averaging the #x# coordinates and #y# coordinates of the vertices.

#x=(5+7+6)/3= 18/3=6#

#y=(1+2+7)/3=10/3#

The coordinates of the centroid are #(6, 10/3)#

To find the distance from the origin, use the distance formula.

#d=sqrt((x_1 - x_2)^2 + (y_1 -y_2)^2)#

#d=sqrt((6-0)^2 +(10/3-0)^2)#

#d=sqrt(36+100/9)#

#d=sqrt(424/9)#

#d=sqrt((4 * 106)/9)#

#d=2/3 sqrt106#