A triangle has corners at #(1 ,6 )#, #(3 ,2 )#, and #(8 ,9 )#. How far is the triangle's centroid from the origin?

1 Answer
Harish Chandra Rajpoot
Jul 22, 2018

#\sqrt{433}/3=6.936\ \text{unit#

Explanation:

Given that the vertices of a triangle are #(x_1, y_1)\equiv(1, 6)#, #(x_2, y_2)\equiv(3, 2)# & #(x_3, y_3)\equiv(8, 9)# then the coordinates of centroid of triangle are given as

#(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3})#

#\equiv (\frac{1+3+8}{3}, \frac{6+2+9}{3})#

#\equiv (4, \frac{17}{3})#

hence the distance between the centroid #(4, 17/3)# & the origin #(0, 0)# is given by distance formula as follows

#\sqrt{(4-0)^2+(17/3-0)^2}#

#=\sqrt{433}/3#

#=6.936\ \text{unit#

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