A line segment has endpoints at #(5 ,6 )# and #(6 , 1)#. The line segment is dilated by a factor of #2 # around #(4 , 2)#. What are the new endpoints and length of the line segment?

1 Answer
Jim G.
Jan 14, 2018

#(6,10),(8,0)#

Explanation:

#"let "A(5,6) ,B(6,1)" and "D(4,2)#

#" then "A'" and "B'" are the images of A and B under"#
#"the dilatation"#

#rArrvec(DA')=color(red)(2)vec(DA)#

#rArrula'-uld=2(ula-uld)#

#rArrula'-uld=2ula-2uld#

#rArrula'=2ula-uld#

#color(white)(xxxx)=2((5),(6))-((4),(2))#

#color(white)(xxxx)=((10),(12))-((4),(2))=((6),(10))#

#rArrA'(6,10)#

#"similarly"#

#vec(DB')=color(red)(2)vec(DB)#

#rArrulb'-uld=2(ulb-uld)#

#rArrulb'=2ulb-uld#

#color(white)(xxxx)=2((6),(1))-((4),(2))=((8),(0))#

#rArrB'(8,0)#

#"to calculate length of segment use the "color(blue)"distance formula"#

#•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#"let "(x_1,y_1)=(6,10)" and "(x_2,y_2)=(8,0)#

#d=sqrt((8-6)^2+(0-10)^2)=sqrt104~~10.2" 1 dec. place"#

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