A triangle has corners at #(-6 ,3 )#, #(3 ,-2 )#, and #(5 ,7 )#. If the triangle is dilated by a factor of #5 # about point #(-2 ,-1 ), how far will its centroid move?

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Answer 1 · 2017-06-19T14:55:27

The distance is #=18.1#

The centroid of the triangle, #A=(-6,3)#, #B=(3,-2)# and #C=(5,7)# is

#C_c=((-6+3+5)/3,(3-2+7)/3)#

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

Let the point #D=(-2,-1)#

Let the centroid be #C_c'# after the dilatation

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

#=5<2/3+2,8/3+1>#

#=<40/3,55/3>#

#C_c'=(40/3,55/3)+(-2,-1)#

#=(34/3,52/3)#

The distance between the centroids is

#d=sqrt((34/3-2/3)^2+(52/3-8/3)^2)#

#=sqrt((32/3)^2+(44/3)^2)#

#=1/3sqrt(32^2+44^2)#

#=1/3sqrt2960#

#=18.1#