A triangle has corners at #(6 ,6 )#, #(7 ,4 )#, and #(5 ,9 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2017-11-06T10:46:23

The triangle's centroid is #8.72# unit from the origin.

Coordinates of the vertices of the triangle are

#A(6,6),B(7,4),C(5,9)#. The coordinates of centroid #(x,y)# of

triangle is the average of the x-coordinate's value and the average

of the y-coordinate's value of all the vertices of the triangle.

#:.x= (6+7+5)/3=6 , y= (6+4+9)/3=6.33(2dp)# .

So centroid is at #(6,6.33)# , Its distance from the origin #(0,0)#

is #D= sqrt((x-0)^2+(y-0)^2) = sqrt((6-0)^2+(6.33-0)^2) # or

#D=sqrt(6^2+6.33^2) =8.72(2dp)# unit.

The triangle's centroid is #8.72(2dp)# unit from the origin [Ans]