A triangle has corners at #(4 ,6 )#, #(3 ,3 )#, and #(6 ,5 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2016-09-11T16:20:02

The centroid coordinates are the average of the coordinates of the vertices; then use the distance formula.

The coordinates of the centroid are the average of the x and y coordinates of the vertices (corners).

Vertices: #(4,6)#, #(3,3)#, #(6,5)#

x coordinate of centroid:
#(4+3+6)/2 = 13/2#

y coordinate of the centroid:
#(6+3+5)/2= 7#

Centroid is located at #(13/2, 7)#

To find the distance from the origin #(0,0)#, use the distance formula.

#sqrt((13/2-0)^2 +(7-0)^2)#

#sqrt(169/4 +49)#

#sqrt(365/4)#

#sqrt365/2#