A line segment has endpoints at #(2 ,7 )# and #(5 ,4 )#. The line segment is dilated by a factor of #2 # around #(4 ,3 )#. What are the new endpoints and length of the line segment?

1 Answer
sankarankalyanam
Jun 10, 2018

#color(violet)("New end points are " (0,110, (6,5) " and the length of the line segment is " 8.49#

Explanation:

#A(2,7), B(5,4), " about "C(4,3) " & dilated by factor " 2#

#A'((x),(y)) = 2a -c = 2 * ((2),(7)) - ((4),(3)) = ((0), (11))#

#B'((x),(y)) = 2b -c = 2 * ((5),(4)) - ((4),(3)) = ((6), (5))#

#"Length of the line segment after dilation " = vec(A'B')#

#vec (A'B') = sqrt((0-6)^2 = (11-5)^2) = 8.49#

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