A triangle has corners at #(1 ,3 )#, #(4 ,-2 )#, and #(-8 ,5 )#. 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 · 2017-07-07T10:37:00

The centroid will move by #=28.3#

The centroid of the triangle, #A=(1,3)#, #B=(4,-2)# and #C=(-8,5)# is

#C_c=((1+4-8)/3,(3-2+5)/3)#

#=(-1,2)#

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

Let the centroid be #C_c'# after the dilatation

#vec(DC_c')=5vec(DC_c)#

#=5<-1-4,2+3>#

#=<-25,25>#

#C_c'=(-25,25)+(4,-3)#

#=(-21,22)#

The distance between the centroids is

#d=sqrt((-21+1)^2+(22-2)^2)#

#=sqrt((-20)^2+(20)^2)#

#=sqrt800#

#=28.3#