A triangle has corners at #(6 ,5 )#, #(1 ,-6 )#, and #(-2 ,9 )#. If the triangle is dilated by a factor of #5 # about point #(5 ,-5 ), how far will its centroid move?

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Answer 1 · 2018-02-10T08:03:11

Centroid moves by #~~ color(green)(33.44)# due to dilation factor of 5 about point #((5),(-5))#

Centroid #G( ((6+1-2)/3),((5-6+9)/3)) = ((5/3),(8/3))#

Dilated about #((5),(-5))# by a factor of 5

New coordinates of centroid G'

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

((x-5),(y+5)) -> 5((5/3 - 5),(8/3+5)) = ((50/3),(115/3))#

#G'((x),(y)) = ((15),(100/3))#

Distance between G & G'

#vec(GG') = sqrt((15-5/3)^2 + (100/3-8/3)^2) ~~ color(green)(33.44)#