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

1 Answer
CW
Apr 18, 2018

#(8sqrt2)/3#

Explanation:

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Let #G(x_a,y_a)# be the centroid of #DeltaABC#, as shown in the figure,
#G(x_a,y_a)=((5+4+8)/3, (3+6+5)/3)=(17/3,14/3)#
Let #D(3,2)# be the center of dilation.
Let #d# be the distance between #D and G#,
#=> d=sqrt((17/3-3)^2+(14/3-2)^2)=(8sqrt2)/3# units
given that the scale factor #k=2#,
#=># the centroid #G# will move by #(k-1)xxd=(2-1)xx(8sqrt2)/3=(8sqrt2)/3# units

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