A line segment has endpoints at #(3 ,2 )# and #(6 ,8 )#. The line segment is dilated by a factor of #4 # around #(1 ,3 )#. What are the new endpoints and length of the line segment?

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Answer 1 · 2017-03-19T07:00:49

The new end points are #(9,-1)# and #(21,23)#
The length of the line segment is #=26.8#

Let #AB# be the line segment

#A=(3.2)#

#B=(6,8)#

Let #A'B'# be the line segment after the dilatation #X4#

The center of dilatation is #D=(1,3)#

#vec(DA')=4vec(DA)=4*<2,-1> = <8,-4>#

#A'=(8+1,-4+3)=(9,-1)#

#vec(DB')=4vec(DB)=4*<5,5> = <20,20>#

#B'=(20+1,20+3)=(21,23)#

The length of the line segment

#A'B'=sqrt((21-9)^2+(23+1)^2)#

#=sqrt(12^2+24^2)=26.8#