A line segment has endpoints at #(5 ,9 )# and #(8 ,2 )#. The line segment is dilated by a factor of #2 # around #(5 ,3 )#. What are the new endpoints and length of the line segment?

1 Answer
sankarankalyanam
Jul 17, 2018

#color(cyan)("New end points are " (5,15), (11,1)#

#color(cyan)("Length of the line segment '" ~~ 15.2315#

Explanation:

#A(5,9), B(8,2), " about point " D (5,3), " dilation factor " 2#

#A'((x),(y)) =(2)a - (1)d =(2)* ((5),(9)) - (1)*((5),(3)) = ((5),(15))#

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

#color(cyan)("New end points are " (5,15), (11,1)#

#color(cyan)("Length of the line segment '" = sqrt((5-11)^2 + (15-1)^2) ~~ 15.2315#

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