A line segment has endpoints at #(5 ,6 )# and #(7 , 3)#. 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
sankarankalyanam
Jul 14, 2018

#color(indigo)("New end points are " (6,10), (0,0)#

#color(indigo)("Length of the line segment '" = sqrt((6)^2 + (10)^2) ~~ 11.6619#

Explanation:

#A(5,6), B(7,3), " about point " D (4,2), " dilation factor " 2#

#A'((x),(y)) =(2)a - (1)d =(2)* ((5),(6)) - (1)*((4),(2)) = ((6),(10))#

#B'((x),(y)) = (2)b - (1)d = (2)* ((2),(1)) - (1)*((4),(2)) = ((0),(0)#

#color(indigo)("New end points are " (6,10), (0,0)#

#color(indigo)("Length of the line segment '" = sqrt((6)^2 + (10)^2) ~~ 11.6619#

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