A triangle has corners at #(2 ,3 )#, #(4 ,-1 )#, and #(-8 ,6 )#. If the triangle is dilated by a factor of #5 # about point #(4 ,-3 ), how far will its centroid move?

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Answer 1 · 2017-07-03T06:47:29

The centroid will move by #=33.4#

The centroid of the triangle, #A=(2,3)#, #B=(4,-1)# and #C=(-8,6)# is

#C_c=((2+4-8)/3,(3-1+6)/3)#

#=(-2/3,8/3)#

Let the point #D=(4,-3)#

Let the centroid be #C_c'# after the dilatation

#vec(DC_c')=4vec(DC_c)#

#=5<-2/3-4,8/3+3>#

#=<-70/3,85/3>#

#C_c'=(-70/3,85/3)+(4,-3)#

#=(-58/3,74/3)#

The distance between the centroids is

#d=sqrt((-58/3+2/3)^2+(74/3+3)^2)#

#=sqrt((56/3)^2+(83/3)^2)#

#=(sqrt10025)/3#

#=33.4#