A triangle has corners at #(4 ,1 )#, #(8 ,3 )#, and #(3 ,8 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2018-05-07T11:43:25

The triangle's centroid is #6.4 # unit from the origin.

Coordinates of the vertices of the triangle are

#A(4,1),B(8,3),C(3,8)#. 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= (4+8+3)/3=5 , y= (1+3+8)/3=4:. (x,y) = (5,4)# .

So centroid is at #(5,4)# and its distance from the origin #(0,0)#

is #D= sqrt((x-0)^2+(y-0)^2) = sqrt((5-0)^2+(4-0)^2) # or

#D=sqrt 41 =6.40 (2dp)# unit.

The triangle's centroid is #6.4 # unit from the origin [Ans]