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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?

Answer 1

Savannah Aguilar

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#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.