A triangle as corners at $(2, 5)$ $(2 ,5 )$ , $(7, 2)$ $(7 ,2)$ , and $(3, 1)$ $(3 ,1)$ . If the triangle is dilated by a factor of $4$ $4$ about #(1 ,9), how far will its centroid move?

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Answer 1 · 2018-02-10T02:11:03

Distance moved by centroid due to dilation factor 4 is

$color(green)(GG' ~~ 16.36)$

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Centroid $G((x),(y)) -> (((2+7+3)/3),((5+2+1)/3) )=> ((4), (8/3))$

$color(blue)(G ((4),(8/3))$

Dilated about point D ((1),(9))# by a factor of 4

$vec(G'D) = 4 * vec(GD)$

$((x - 1),(y - 9)) = 4 * ((4-1),(8/3-9)) => 4 ((3),(-19/3))$

$x - 1 = 4 * 3 = 12, x = 13$

$y - 9 = 4 * (-19/3) = -76/3, y = 49/3$

$color(blue)(G'((13),(49/3))$

Distance moved by G to G'

$vec(GG' )= sqrt((13-4)^2 + (49/3 - 8/3)^2) ~~ color(brown)(16.36)$

A triangle as corners at (2 ,5 )(2,5)(2 ,5 ), (7 ,2)(7,2)(7 ,2), and (3 ,1)(3,1)(3 ,1). If the triangle is dilated by a factor of 4 44 about #(1 ,9), how far will its centroid move?