A triangle has corners at $(7 ,8 )$ , $(2 ,4 )$ , and $(6 ,3 )$ . If the triangle is dilated by a factor of $2$ about point #(6 ,12 ), how far will its centroid move?

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Answer 1 · 2018-02-10T08:33:11

Distance moved by centroid $~~ color(green)(20.25)$

Centroid $G ((7+2+6)/3,(8+4+3)/3)) => ((5),(5))$

Dilation factor 2, dilated about D (6,12)

To find new coordinates of centroid G'

$vec(G'D) = 2 * vec(GD)$

$G'((x-6),(y-12)) = 2 * ((5-6),(5-12)) => ((-2),(-14))$

$G'((5),(-1))$

$vec(GG') = sqrt((-2-5)^2 + (-14-5)^2) ~~ color(green)(20.25)$

A triangle has corners at (7 ,8 )(7 ,8 ), (2 ,4 )(2 ,4 ), and (6 ,3 )(6 ,3 ). If the triangle is dilated by a factor of 2 2 about point #(6 ,12 ), how far will its centroid move?