A triangle has corners at #(5 ,2 )#, #(-3 ,-3 )#, and #(1 ,-2 )#. If the triangle is dilated by a factor of #1/3 # about point #(5 ,-2 ), how far will its centroid move?

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Answer 1 · 2017-05-12T15:27:28

The centroid will move by #=sqrt68/3=2.75#

The centroid of the triangle, #A=(5,2)#, #B=(-3,-3)# and #C=(1,-2)# is

#C_c=((5-3+1)/3,(2-3-2)/3)#

#=(1,-1)#

Let the point #D=(5,-2)#

Let the centroid be #C_c'# after the dilatation

#vec(DC_c')=1/3vec(DC_c)#

#=1/3<1-5,-1+2>#

#=<-4/3,1/3>#

#C_c'=(-4/3,1/3)+(5,-2)#

#=(11/3,-5/3)#

The distance between the centroids is

#d=sqrt((11/3-1)^2+(-5/3+1)^2)#

#=sqrt(64/9+4/9)#

#=sqrt68/3#

#=2.75#