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

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Answer 1 · 2016-11-28T20:16:00

#"the new end points are:"A'(7,19),B'(-1,11)#

#"length of the new line segment is :"8sqrt 2#

#"1- draw Point objects A(4,7),B(2,5),D(3,3) and line segment"#

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#"2-find the new location of the Point B"#

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#x=3-1*4=3-4=-1#

#y=3+2*4=3+8=11#

#"the new location of B is "B'(-1,11)#

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#"3-find the new location of A" #

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#x=3+1*4=3+4=7#

#y=3+4*4=3+16=19#

#A'(7,19)#

#"4-draw the new line segment "A'(7,19),B'(-1,11)#

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#"length of the new line segment :"#

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#A'B'=sqrt((19-11)^2+(7+1)^2)#

#A'B'=sqrt(8^2+8^2)#

#A'B'=sqrt(64+64)#

#A'B'=8sqrt2#