A line segment has endpoints at #(4 ,3 )# 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?

1 Answer
sankarankalyanam
Jul 14, 2018

#color(purple)("New coordinates are " (7, 3), (-1, 11)#

#color(purple)("Length of the line segment '" = sqrt((7 - -1)^2 + (3-11)^2) ~~ 11.3137#

Explanation:

#A(8,4), B(4,3), " about point " D (1,3), " dilation factor "4#

#A'((x),(y)) =(4)a - (3)d =(4)*((4),(3)) - (3)*((3),(3)) = ((7),(3))#

#B'((x),(y)) = (4)b - (3)d = (4)*((2),(5)) - (3)*((3),(3)) = ((-1),(11))#

#color(purple)("New coordinates are " (7, 3), (-1, 11)#

#color(purple)("Length of the line segment '" = sqrt((7 - -1)^2 + (3-11)^2) ~~ 11.3137#

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