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)#