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A triangle has corners at #(5 ,3 )#, #(9 ,2 )#, and #(6 ,7 )#. How far is the triangle's centroid from the origin?

Answer 1

Claire Akin

#sqrt 544 /3#

The coordinates of the centroid would be # ((5+9+6)/3, (3+2+7)/3)# or #(20/3 , 4)#

Distance from the origin would be #sqrt((20/3)^2 +4^2)= sqrt(544/9)= sqrt 544/3#

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Answer 2

Mason Adams

To find the centroid of a triangle, you take the average of the coordinates of its vertices.

Centroid coordinates = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3)

Given vertices: (5, 3), (9, 2), and (6, 7)

Centroid coordinates = ((5 + 9 + 6)/3, (3 + 2 + 7)/3) = (20/3, 12/3) = (20/3, 4)

Using the distance formula, the distance between the centroid and the origin is √((20/3)^2 + 4^2).

Distance = √((20/3)^2 + 4^2) ≈ √(400/9 + 16) ≈ √(444/9) ≈ √(444)/3 ≈ 2√(111)/3

So, the distance between the centroid and the origin is approximately 2√(111)/3.

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Answer from HIX Tutor

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