What is the centroid of a triangle with corners at #(4, 7 )#, #(1,2 )#, and #(8 , 5 )#?

Question

What is the centroid of a triangle with corners at #(5, 1)#, #(4, 9)#, and #(7,2)#?
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What is the centroid of a triangle with corners at #(6, 1 )#, #(2, 2 )#, and #(1 , 6 )#?
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What is the centroid of a triangle with corners at #(3, 2 )#, #(5,5 )#, and #(12 , 9 )#?
What is the centroid of a triangle with corners at #(3, 2 )#, #(1,5 )#, and #(0 , 9 )#?
What is the centroid of a triangle with corners at #(2, 7 )#, #(1,5 )#, and #(7 , 5 )#?

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Answer 1 · 2016-05-17T11:29:10

Centroid of the triangle is#(4 1/3,4 2/3)#

he centroid of a triangle whose vertices are #(x_1,y_1)#, #(x_2,y_2)# and (x_3,y_3)# is given by

#((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)#

Hence centrid of given triangle is #((4+1+8)/3,(7+2+5)/3)# or #(13/3,14/3)# or #(4 1/3,4 2/3)#.