A line segment has endpoints at #(0 ,9 )# and #(8 ,2 )#. The line segment is dilated by a factor of #2 # around #(5 ,1 )#. What are the new endpoints and length of the line segment?

1 Answer
sankarankalyanam
Jul 14, 2018

#color(blue)("New end points are " (-5,17), (11,3)#

#color(blue)("Length of the line segment '" = ~~ 22.0227#

Explanation:

#A(0,9), B(8,2), " about point " D (5,1), " dilation factor " 2#

#A'((x),(y)) =(2)a - (1)d =(2)* ((0),(9)) - (1)*((5),(1)) = ((-5),(17))#

#B'((x),(y)) = (2)b - (1)d = (2)* ((8),(2)) - (1)*((5),(1)) = ((11),(3)#

#color(blue)("New end points are " (-5,17), (11,3)#

#color(blue)("Length of the line segment '" = sqrt((-5-11)^2 + (17-3)^2) ~~ 22.0227#

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