A triangle has corners at #(2 ,3 )#, #(1 ,-2 )#, and #(-6 ,6 )#. If the triangle is dilated by a factor of #5 # about point #(-3 ,2 ), how far will its centroid move?

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Answer 1 · 2017-12-20T13:37:33

The centroid will move by #=4/3sqrt37#

The corners of the triangle are #A=(2,3)#, #B=(1,-2)# and #C=(-6,6)#

The centroid of triangle #ABC# is

#C=((2+1-6)/3, (3-2+6)/3)=(-1,7/3)#

Let the the new centroid be #C'=(x,y)# after dilatation.

Let the fixed point be #D=(-3,2)#

Let the coefficient of dilatation be #k=5#

Therefore, in vector notation

#vec(DC')=kvec(DC)#

#((x-(-3)),(y-2))=5((-1-(-3)),(7/3-2))#

#x+3=5*2#, #=>#, #x=7#

#y-2=5*(1/3)#, #=>#, #y=11/3#

The centroid will move by

#=sqrt((7+1)^2+(11/3-7/3)^2)#

#=sqrt(64+16/9)#

#=sqrt(592/9)#

#=4/3sqrt37#