A triangle has corners at #(-2 ,6 )#, #(4 ,-3 )#, and #(2 ,9 )#. If the triangle is dilated by a factor of #5 # about point #(-5 ,6 ), how far will its centroid move?

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Answer 1 · 2017-06-20T19:51:35

The centroid will move by #=26.6#

The centroid of the triangle, #A=(-2,6)#, #B=(4,-3)# and #C=(2,9)# is

#C_c=((-2+4+2)/3,(6-3+9)/3)#

#=(4/3,4)#

Let the point #D=(-5,6)#

Let the centroid be #C_c'# after the dilatation

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

#=5<4/3+5,4-6>#

#=<95/3,-10>#

#C_c'=(95/3,-10)+(-5,6)#

#=(80/3,-4)#

The distance between the centroids is

#d=sqrt((80/3-4/3)^2+(-4-4)^2)#

#=sqrt((76/3)^2+(8)^2)#

#=sqrt(705.8)#

#=26.6#