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

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Answer 1 · 2018-04-25T02:13:20

${10 sqrt(5) }/3$

Centroid $C=( (1 + -3 + 7)/3 , (5 + -4 + -2)/3 ) = (5/3, -1/3)$

Dilation point: $D(-5,3)$

Distance $DC = \sqrt{ (-5 -5/3)^2 + (3 - -1/3)^2 } = {10 sqrt(5) }/3$

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

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?