A triangle as corners at #(1 ,7 )#, #(4 ,3 )#, and #(2 ,6 )#. If the triangle is dilated by a factor of #3 # about #(4 ,2 ), how far will its centroid move?

1 Answer
Dean R.
Apr 25, 2018

# {10 \sqrt{5}}/3 #

Explanation:

The centroid is the average of the coordinates:

#C = ( (1+4+2)/3, (7+3+6)/3) = (7/3, 16/3)#

That's a distance from the dilation point #D(4,2)# of

# d = sqrt{(4-7/3)^2 + (2-16/3)^2 } = { 5 sqrt{5} }/3 #

# C# is currently #1 d# away from #D#, after dilation it will be #3d# away from #D#, so it will have moved by

#2d = {10 \sqrt{5}}/3 #

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