A line segment has endpoints at #(5 ,8 )# and #(2 , 1)#. The line segment is dilated by a factor of #2 # around #(3 , 5)#. What are the new endpoints and length of the line segment?

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Answer 1 · 2017-05-09T13:33:53

The new endpoints are #=(7,11)# and #=(1,-3)#
The length of the segment is #=sqrt232=15.2#

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

#A=(5,8)#

#B=(2,1)#

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

Let the point #C=(3,5)#

Then,

#vec(CA')=2vec(CA)=2*<5-3,8-5> = <4,6>#

#A'=(4,6)+(3,5)=(7,11)#

Similarly,

#vec(CB')=2vec(CB)=2*<2-3,1-5> = <-2,-8>#

#B'=(-2,-8)+(3,5)=(1,-3)#

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

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

#=sqrt(36+196)#

#=sqrt232#