A triangle has corners at #(5 ,2 )#, #(4 ,6 )#, and #(3 ,1 )#. How far is the triangle's centroid from the origin?

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Answer 1 · 2016-12-16T10:24:10

#|d|=5" "unit#

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#"let the triangle's centroid be D(x,y)"#

#A(x_1,y_1)" ; "B(x_2,y_2)" ; "C(x_3,y_3)#

#D((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)#

#x=((4+5+3)/3)=4#

#y=((6+2+1)/3)=3#

#"thus " D(4,3)#

#"now;let's calculate d"#

#|d|=sqrt((4-0)^2+(3-0)^2)#

#|d|=sqrt(4^2+3^2)#

#|d|=sqrt(16+9)#

#|d|=sqrt(25)#

#|d|=5" "unit#