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

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Answer 1 · 2017-05-10T06:35:17

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:

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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#