A triangle has corners at (8 ,3 )(8,3), (4 ,-6 )(4,−6), and (-2 ,5 )(−2,5). If the triangle is dilated by a factor of 5 5 about point #(1 ,-3 ), how far will its centroid move?

1 Answer
Ananda Dasgupta
Aug 3, 2016

4/3sqrt{170}43√170

Explanation:

The centroid of the triangle is originally at

({8+4+(-2)}/3,{3+(-6)+5}/3)=(10/3,2/3)(8+4+(−2)3,3+(−6)+53)=(103,23)

The distance of the centroid from (1,-3)(1,−3) is

sqrt{(10/3-1)^2+(2/3-(-3))^2}=1/3sqrt{7^2+11^2}=1/3sqrt{170}√(103−1)2+(23−(−3))2=13√72+112=13√170

This distance is multiplied by a factor of 5 by the dilatation. The distance the centroid will move is
4 xx 1/3 sqrt{170} = 4/3sqrt{170}4×13√170=43√170

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