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

1 Answer
sankarankalyanam
Jul 14, 2018

#color(violet)("New end points are " (3/2, 7/2), (5/2,3)#

#color(violet)("Length of the line segment '" = sqrt((3/2- 5/2)^2 + (7/2-3)^2) ~~ 1.118#

Explanation:

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

#A'((x),(y)) =(1/2)a - (-1/2)d =(1/2)* ((1),(2)) - (-1/2)*((2),(5)) = ((3/2),(7/2))#

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

#color(violet)("New end points are " (3/2, 7/2), (5/2,3)#

#color(violet)("Length of the line segment '" = sqrt((3/2- 5/2)^2 + (7/2-3)^2) ~~ 1.118#

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