A triangle has corners at #(4 ,6 )#, #(3 ,9 )#, and #(6 ,5 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2017-09-01T12:09:31

The triangle's centroid is #7.95# unit far from the origin #(0,0)#

Corners of triangle co-ordinates are

#A(x_1=4, y_1=6) , B(x_2=3, y_2=9),C(x_3=6, y_3=5)#

We know centroid #(x)=(x_1+x_2+x_3)/3 = (4+3+6)/3= 13/3# and

centroid #(y)=(y_1+y_2+y_3)/3 = (6+9+5)/3= 20/3#

So centroid co-ordinates are # (x=13/3,y=20/3)#

Distance of centroid from origin#(0,0)# is

#D= sqrt((x-0)^2+(y-0)^2) =sqrt((13/3)^2 +(20/3)^2) ~~ 7.95# unit

The triangle's centroid is #7.95# unit far from the origin #(0,0)# [Ans]