A line segment has endpoints at #(2 ,7 )# and #(8 ,2 )#. The line segment is dilated by a factor of #2 # around #(1 ,1 )#. What are the new endpoints and length of the line segment?

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Answer 1 · 2017-05-11T13:11:53

The new end points are #(3,13)# and #(15,3)#
The length of the line segment is # =sqrt244=15.6#

Let the endpoints of the segment be #A# an #B#

#A=(2,7)#

#B=(8,2)#

Let the endpoints after dilatation be #A'# and #B'#

Let the point #C=(1,1)#

Then,

#vec(CA')=2vec(CA)=2*<2-1,7-1> = <2,12>#

#A'=(2,12)+(1,1)=(3,13)#

Similarly,

#vec(CB')=2vec(CB)=2*<8-1,2-1> = <14,2>#

#B'=(14,2)+(1,1)=(15,3)#

The length of the segment #A'B'# is

#=sqrt((15-3)^2+(3-13)^2)#

#=sqrt(144+100)#

#=sqrt244#