A line segment has endpoints at #(4 ,3 )# and #(3 ,9 )#. The line segment is dilated by a factor of #4 # around #(2 ,2 )#. What are the new endpoints and length of the line segment?

1 Answer
Jim G.
Jun 23, 2017

#(10,6),(6,30),~~24.33#

Explanation:

#"let " A(4,3),B(3,9),D(2,2)" and " A',B'#
#"be the image of A and B under the dilatation"#

#vec(DA)=ula-uld=((4),(3))-((2),(2))=((2),(1))#

#rArrvec(DA')=color(red)(4)vec(DA)=color(red)(4)((2),(1))=((8),(4))#

#rArrA'=(2+8,2+4)=(10,6)#

#vec(DB)=ulb-uld=((3),(9))-((2),(2))=((1),(7))#

#rArrvec(DB')=color(red)(4)vec(DB)=color(red)(4)((1),(7))=((4),(28))#

#rArrB'=(2+4,2+28)=(6,30)#

#|A'B'|=sqrt((6-10)^2+(30-6)^2)=sqrt592#

#rArr|A'B'| ~~24.33" to 2 decimal places"#

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