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

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Answer 1 · 2016-08-03T15:28:35

$4/3sqrt{170}$

The centroid of the triangle is originally at

$({8+4+(-2)}/3,{3+(-6)+5}/3)=(10/3,2/3)$

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

$sqrt{(10/3-1)^2+(2/3-(-3))^2}=1/3sqrt{7^2+11^2}=1/3sqrt{170}$

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

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?