A line segment has endpoints at #(5 ,8 )# and #(2 , 1)#. The line segment is dilated by a factor of #1/2 # around #(3 , 5)#. What are the new endpoints and length of the line segment?

1 Answer
sankarankalyanam
Jul 14, 2018

#color(brown)("New end points are " (4,13/2), (5/2, 3)#

#color(brown)("Length of the line segment '" = sqrt((4- 5/2)^2 + (13/2-3)^2) ~~ 3.8079#

Explanation:

#A(5,8), B(2,1), " about point " D (3,5), " dilation factor " 1/2#

#A'((x),(y)) =(1/2)a - (-1/2)d =(1/2)* ((5),(8)) - (-1/2)*((3),(5)) = ((4),(13/2))#

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

#color(brown)("New end points are " (4,13/2), (5/2, 3)#

#color(brown)("Length of the line segment '" = sqrt((4- 5/2)^2 + (13/2-3)^2) ~~ 3.8079#

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