A triangle has corners at (1 ,5 )(1,5), (-3 ,-4 )(−3,−4), and (7 ,-2 )(7,−2). If the triangle is dilated by a factor of 2 2 about point (-5 ,3)(−5,3), how far will its centroid move?

1 Answer
Dean R.
Apr 25, 2018

{10 sqrt(5) }/310√53

Explanation:

Centroid C=( (1 + -3 + 7)/3 , (5 + -4 + -2)/3 ) = (5/3, -1/3) C=(1+−3+73,5+−4+−23)=(53,−13)

Dilation point: D(-5,3)D(−5,3)

Distance DC = \sqrt{ (-5 -5/3)^2 + (3 - -1/3)^2 } = {10 sqrt(5) }/3DC=√(−5−53)2+(3−−13)2=10√53

If we're dilating by a factor of two, we'll go from that distance away to twice that distance, moving by that distance.

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