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

Answer 1

James Atkins

Centroid is #"at "(6, 4)#; distance to #(0, 0)# is #2sqrt(13)~~7.2#

To find the centroid you need to find the midpoints using #((x_1 + x_2)/2, (y_1 + y_2)/2)#

Midpoint between #(3,2) " and " (9, 3) = (6, 2.5)#

Midpoint between #(3,2) " and " (6, 7) = (4.5, 4.5)#

Midpoint between #(6,7) " and " (9, 3) = (7.5, 5)#

Connect the midpoints to the angle opposite. The intersection is the centroid:

The centroid is found at #(6, 4)#

The distance from #(6, 4) " and "(0,0) = sqrt(6^2 + 4^2) = sqrt(52) = 2 sqrt(13) ~~ 7.2#

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Answer 2

Evelyn Arboleda

To find the centroid of a triangle, you can calculate the average of the coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin. The formula for the distance between two points (x1, y1) and (x2, y2) is given by:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

After calculating the centroid's coordinates, you can use the distance formula with the coordinates of the centroid and the origin (0, 0) to find the distance.

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