A line segment has endpoints at #(7 ,6 )# and #(5 ,8 )#. The line segment is dilated by a factor of #3 # around #(2 ,4 )#. What are the new endpoints and length of the line segment?

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Answer 1 · 2017-05-07T09:55:33

The new emd points are #(17,10)# and #(11,16)#
The length of the line segment is #=8.49#

Let the end points be#A=(7,6)# and #B=(5,8)#

and #C=(2,4)#

Let #A'# and #B'# be the new end points

Then,

#vec(CA')=3vec(CA)#

#=3*<7-2,6-4> =3*<5,2> = <15,6>#

#A'=(15,6)+(2,4)=(17,10)#

Similarly,

#vec(CB')=3vec(CB)#

#=3*<5-2,8-4> =3*<3,4> = <9,12>#

#B'=(9,12)+(2,4)=(11,16)#

The length of the line segment is

#A'B'=sqrt((11-17)^2+(16-10)^2)#

#=sqrt((6)^2+(6)^2)#

#=sqrt72#

#=8.49#

The length of the old line segment is

#AB=sqrt((5-7)^2+(8-6)^2)#

#=sqrt(4+4)#

#=sqrt(8)#

#=2.83#

#A'B'=3*AB#