A triangle has corners at #(5 ,2 )#, #(4 ,6 )#, and #(8 ,5 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2016-10-05T17:16:48

The distance is #~~ 7.13#

Centroid coordinates given the vertices is a reference for the equations that I will use.

Let #(O_x, O_y)# be the centroid and #(A_x, A_y)#, #(B_x, B_y)#, and00 #(C_x, C_y)# be the vertices then:

#O_x = (A_x + B_x + C_x)/3#

and

#O_y = (A_y + B_y + C_y)/3#

#O_x = (5 + 4 + 8)/3 = 17/3#

and

#O_y = (2 + 6 + 5)/3 = 13/3#

The distance from the origin is:

#d = sqrt((17/3)² + (13/3)²)#

#d ~~ 7.13 #