A triangle has corners at #(2 ,4 )#, #(7 ,6 )#, and #(4 ,5 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2017-12-01T11:03:35

The triangle's centroid is #6.62(2dp)# unit from the origin.

Coordinates of the vertices of the triangle are

#A(2,4),B(7,6),C(4,5)#. 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= (2+7+4)/3=13/3=4 1/3 , y= (4+6+5)/3=5 # .

So centroid is at #(4 1/3,5)# , Its distance from the origin #(0,0)#

is #D= sqrt((x-0)^2+(y-0)^2) = sqrt((13/3-0)^2+(5-0)^2) # or

#D=sqrt((13/3)^2+5^2) ~~6.62(2dp)# unit.

The triangle's centroid is #6.62(2dp)# unit from the origin [Ans]