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

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Answer 1 · 2018-02-04T08:39:26

Distance of centroid from origin is

#OG = d = sqrt((13/3)^2 + 5^2) = color(purple)(6.6165)#

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Formula for finding the centroid coordinates.

#G_x = (x1 + x2 + x3)/3 = (6 + 2 + 5) / 3 = 13/3#

#G_y = (y1 + y2 + y3) / 3 = (7 + 6 + 2) / 3 = 5#

Centroid coordinates #G(13/3, 5)#

Distance from origin #O(0,0)# is

#d = sqrt((13/3)^2 + 5^2) = color(purple)(6.6165)#