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

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Answer 1 · 2018-02-10T07:46:35

Distance moved by centroid $~~ color(green)(2.53$

Formila for finding coordinates of centroid

$G(((x_1 + x_2 + x_3) /c),((y_1 + y_2 + y_3)/3)) = (((4+3+8)/3),((-6-3+4)/2)) = ((5),(-5/3))$

Dilated around point $((-3),(2))$ by a factor of (1/3)#

New coordinates of centroid $vec(G'D)((x+3),(y-2)) = (1/3)vec(GD) = (1/3)((5+3),(-5/3-2)) => ((8/3),(-11/9))$

$G' ((17/3),(7/9))$

Distance between G & G'

$vec(GG') = sqrt((17/3-5)^2 + (7/9 + 5/3)^2) = sqrt((7/5)^2 + (4/9)^2) = ~~ color(green)(2.53$

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