A triangle has corners at $(2, 1)$ $(2 ,1 )$ , $(4, - 3)$ $(4 ,-3 )$ , and $(- 1, 4)$ $(-1 ,4 )$ . If the triangle is dilated by a factor of $5$ $5$ about point #(4 ,-9 ), how far will its centroid move?

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Answer 1 · 2018-02-10T08:49:09

Centroid moves by $\approx 54.62$ $~~ color(green)(54.62)$

Centroid $G(((2+4-1)/3),((1-3+4)/3)) => ((-5/3),(2/3))$

Dilated about D(4-9) by a factor of 5

To find new coordinate of centroid G'

$vec(G'D) = 5 * vec(GD)$

$G'((x-4),(y+9)) = 5 * ((-5/3-4),(2/3+9))=> ((-85/3),(145/3))$

$G' ((-73/3),(118/3))$

$vec(GG') = sqrt((-5/3+85/3)^2 + (2/3-145/3)^2) ~~ color(green)(54.62)$

A triangle has corners at (2 ,1 )(2,1)(2 ,1 ), (4 ,-3 )(4,−3)(4 ,-3 ), and (-1 ,4 )(−1,4)(-1 ,4 ). If the triangle is dilated by a factor of 5 55 about point #(4 ,-9 ), how far will its centroid move?