A triangle has corners at #(5 ,6 )#, #(3 ,7 )#, and #(8 ,9 )#. How far is the triangle's centroid from the origin?

Answer 1

Avery Allen

The answer is #=9.1#

The centroid#(x_c,y_c)# of a triangle with corners #(x_1,y_1)#, #(x_2,y_2)# and #(x_3,y_3)# is

#x_c=(x_1+x_2+x_3)/3#

#y_c=(y_1+y_2+y_3)/3#

Therefore,

#x_c=(5+3+8)/3=16/3#

#y_c=(6+7+9)/3=22/3#

The distance from the origin is

#=sqrt(x_c^2+y_c^2)#

#=sqrt(16^2/9+22^2/9)#

#=sqrt(16^2+22^2)/3#

#=sqrt740/3=9.1#

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Answer 2

Aurora Ayala

The centroid of a triangle is located at the average of its vertices' coordinates. So, to find the centroid, calculate the average of the x-coordinates and the average of the y-coordinates of the vertices. Then, use the distance formula to find the distance between the centroid and the origin, which is (0, 0).

Centroid coordinates: x-coordinate = (5 + 3 + 8) / 3 = 16 / 3 y-coordinate = (6 + 7 + 9) / 3 = 22 / 3

Distance from the origin: √((16/3)^2 + (22/3)^2) ≈ 7.72 units

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Answer from HIX Tutor

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