A triangle as corners at #(3 ,5 )#, #(5 ,2)#, and #(9 ,4)#. If the triangle is dilated by a factor of #4 # about #(1 ,9), how far will its centroid move?

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Answer 1 · 2017-06-12T12:51:30

The centroid will move by #=21.3#

The centroid of the triangle, #A=(3,5)#, #B=(5,2)# and #C=(9,4)# is

#C_c=((3+5+9)/3,(5+2+4)/3)#

#=(17/3,11/3)#

Let the point #D=(1,9)#

Let the centroid be #C_c'# after the dilatation

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

#=4<17/3-1,11/3-9>#

#=<56/3,-64/3>#

#C_c'=(56/3,-64/3)+(1,9)#

#=(59/3,-37/3)#

The distance between the centroids is

#d=sqrt((59/3-17/3)^2+(-37/3-11/3)^2)#

#=sqrt((42/3)^2+(48/3)^2)#

#=sqrt(14^2+16^2)#

#=sqrt452#

#=21.3#