A triangle has corners at #(1 ,3 )#, #(7 ,7 )#, and #(8 ,5 )#. If the triangle is dilated by a factor of #2 # about point #(3 ,5 ), how far will its centroid move?

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Answer 1 · 2018-01-04T10:13:45

let the centroid of the triangle = #C(x,y)#
Then,
Co-ordinate of #C(x,y)#= #((1+7+8)/3# , #(3+7+5)/3)#
C#(x,y)#= #(16/3, 5)#

Let us consider centroid #C'(x',y')# after the triangle is dilated by a factor of 2 about point #D(3,5)#

Now, we can write,

#vec(DC')=2*vec(DC)#

#(x'-3 ,y'-5)#=#2*(16/3-3 ,5-5)#

#x'-3=2*(16/3-3)#
#rArrx'=14/3+3#

#rArrx'=23/3#

Similarly
#y'-5=2*0#

#rArry'=5#

Therefore new centroid #C'(x',y')=(23/3,5)#
Now,
The distance between the centroids is
#CC'=sqrt((5-5)^2+(23/3-16/3)^2)#
#CC'=7/3#
#CC'=2.333#