A line segment has endpoints at #(1 ,2 )# and #(3 , 9)#. The line segment is dilated by a factor of #1/2 # around #(4 , 2)#. What are the new endpoints and length of the line segment?

1 Answer
sankarankalyanam
Jul 14, 2018

#color(red)("New end points are " (5/2, 2), (7/2,11/2)#

#color(red)("Length of the line segment '" = sqrt((5/2- 7/2)^2 + (11/2-2)^2) ~~ 3.64#

Explanation:

#A(1,2), B(3,9), " about point " D (4,2), " dilation factor " 1/2#

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

#B'((x),(y)) = (1/2)b - (-1/2)d = (1/2)* ((3),(9)) - (-1/2)*((4),(2)) = ((7/2),(11/2)#

#color(red)("New end points are " (5/2, 2), (7/2,11/2)#

#color(red)("Length of the line segment '" = sqrt((5/2- 7/2)^2 + (11/2-2)^2) ~~ 3.64#

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