A triangle has corners at #(9 ,3 )#, #(2 ,5 )#, and #(3 ,4 )#. How far is the triangle's centroid from the origin?

1 Answer
Alan P.
May 5, 2016

Distance of centroid from origin is (approximately) #6.15# units

Explanation:

The centroid of a triangle with corners at #(x_1,y_1), (x_2,y_2), and (x_3,y_3)# can be located using the formula
#color(white)("XXX")(x_c,y_c)=((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)#

In this case
#color(white)("XXX")(cx_c,y_c)=((9+2+3)/3,(3+5+4)/3)=(14/3,4)#

The distance of the centroid at #(14/3,4)# and the origin at #(0,0)#
can be calculated using the Pythagorean Theorem as
#color(white)("XXX")d=sqrt((14/3)^2+4^2) ~~6.15#

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