A triangle has corners at #(5 ,6 )#, #(2 ,7 )#, and #(3 ,5 )#. How far is the triangle's centroid from the origin?

1 Answer
Harish Chandra Rajpoot
Jul 26, 2018

#2/3\sqrt{106}=6.864\ text{unit##

Explanation:

The coordinates of centroid of given triangle with vertices at #(x_1, y_1)\equiv(5, 6)#, #(x_2, y_2)\equiv(2, 7)# & #(x_3, y_3)\equiv(3, 5)# are given as

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

#\equiv(\frac{5+2+3}{3}, \frac{6+7+5}{3})#

#\equiv(10/3, 6)#

hence the distance of centroid of triangle #(10/3, 6) # from the origin #(0, 0)# is given by using distance formula

#\sqrt{(10/3-0)^2+(6-0)^2}#

#=2/3\sqrt{106}#

#=6.864\ text{unit#

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