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A triangle has corners at #(4 ,1 )#, #(2 ,3 )#, and #(5 ,8 )#. How far is the triangle's centroid from the origin?

Answer 1

Claire Akin

Distance between centroid and origin is # ~~ color(purple)(5.4263)#

Given : A(4,1), B(2,3), C(5,8)

Coordinates of centroid G

#G(x,y) = (x_a + x_a + x_c)/3, (y_a + y_b + y_c)/3#

#G_x = (4 + 2 + 5) / 3 = 11/3#

#G_y = (1 + 3 + 8)/3 = 4#

Distance between centroid G and origin O

#vec(GO) = sqrt((11/3)^2 + 4^2) ~~ color(purple)(5.4263)#

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Answer 2

Jayden Jackson

The distance from the centroid of the triangle to the origin is approximately 3.86 units.

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Answer from HIX Tutor

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