A triangle has corners at #(2 ,3 )#, #(1 ,-2 )#, and #(-6 ,6 )#. If the triangle is dilated by a factor of #5 # about point #(4 ,-3 ), how far will its centroid move?

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Answer 1 · 2017-05-09T07:02:44

The centroid will move by #=33.9#

Let #ABC# be the triangle

#A=(2,3)#

#B=(1,-2)#

#C=(-6,6)#

The centroid of triangle #ABC# is

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

Let the new centroid after the dilatation be #C_c'#

Let the point #D=(4,-3)#

Then,

#vec(DC_c')=5vec(DC_c)=5(-1-4,7/3+3)=(-25,80/3)#

#C_c'=(-25,80/3)+(4,3)=(-21,89/3)#

Therefore,

the distance #C_cC_c'#

#=sqrt((-21+1)^2+(89/3-7/3)^2)#

#=sqrt(400+747.1)#

#=33.9#