A line segment has endpoints at #(8 ,4 )# and #(3 ,7 )#. The line segment is dilated by a factor of #1/2 # around #(3 ,2 )#. What are the new endpoints and length of the line segment?

1 Answer
sankarankalyanam
Jul 14, 2018

#color(purple)("New end points are " (11/2, 3), (3,9/2)#

#color(purple)("Length of the line segment '" = sqrt((11/2- 3)^2 + (3-9/2)^2) ~~ 2.9155#

Explanation:

#A(8,4), B(3,7), " about point " D (3,2), " dilation factor " 1/2#

#A'((x),(y)) =(1/2)a - (-1/2)d =(1/2)* ((8),(4)) - (-1/2)*((3),(2)) = ((11/2),(3))#

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

#color(purple)("New end points are " (11/2, 3), (3,9/2)#

#color(purple)("Length of the line segment '" = sqrt((11/2- 3)^2 + (3-9/2)^2) ~~ 2.9155#

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