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

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Answer 1 · 2017-05-19T13:05:07

The new endpoints are #(13,6)# and #(5,18)#
The length of the line segment is #=sqrt208=14.42#

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

#A=(4,3)#

#B=(2,6)#

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

Let the point #C=(1,2)#

Then,

#vec(CA')=4vec(CA)=4*<4-1,3-2> = <12,4>#

#A'=(12,4)+(1,2)=(13,6)#

Similarly,

#vec(CB')=4vec(CB)=4*<2-1,6-2> = <4,16>#

#B'=(4,16)+(1,2)=(5,18)#

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

#=sqrt((5-13)^2+(18-6)^2)#

#=sqrt(64+144)#

#=sqrt208#