A line segment has endpoints at #(7 ,6 )# and #(5 ,2 )#. The line segment is dilated by a factor of #4 # around #(4 ,3 )#. What are the new endpoints and length of the line segment?

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Answer 1 · 2017-05-12T10:00:34

The new end points are #(16.15)# and #(8,-1)#
The length of the new segment is #=sqrt320=17.9#

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

#A=(7,6)#

#B=(5,2)#

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

Let the point #C=(4,3)#

Then,

#vec(CA')=4vec(CA)=4*<7-4,6-3> = <12,12>#

#A'=(12,12)+(4,3)=(16,15)#

Similarly,

#vec(CB')=4vec(CB)=4*<5-4,2-3> = <4,-4>#

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

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

#=sqrt((16-8)^2+(15+1)^2)#

#=sqrt(64+256)#

#=sqrt320#