A triangle has corners at #(4 ,6 )#, #(3 ,9 )#, and #(7 ,2 )#. How far is the triangle's centroid from the origin?

1 Answer
Harish Chandra Rajpoot
Jul 23, 2018

#7.341\ \text{unit#

Explanation:

Given that the vertices of a triangle are #(x_1, y_1)\equiv(4, 6)#, #(x_2, y_2)\equiv(3, 9)# & #(x_3, y_3)\equiv(7, 2)# 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{4+3+7}{3}, \frac{6+9+2}{3})#

#\equiv (14/3, \frac{17}{3})#

hence the distance between the centroid #(14/3, 17/3)# & the origin #(0, 0)# is given by distance formula as follows

#\sqrt{(14/3-0)^2+(17/3-0)^2}#

#=\sqrt{485}/3#

#=7.341\ \text{unit#

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