A line segment has endpoints at #(4 ,3 )# and #(2 ,6 )#. The line segment is dilated by a factor of #4 # around #(3 ,3 )#. What are the new endpoints and length of the line segment?

1 Answer
sankarankalyanam
Jun 8, 2018

#color(brown)("Length of the line segment after dilation is " #

#color(indigo)(vec(A'B') = 14.42 " units"#

Explanation:

#A(4,3), B(2,6), " dilated by a factor of 4 about " C(3,3)#

#A'((x),(y)) = 4a - 3c = 4 ((4),(3)) - 3 ((3),(3)) = ((7),(3))#

#B'((x),(y)) = 4b - 3c = 4 ((2),(6)) - 3 ((3),(3)) = ((-1),(15))#

#color(brown)(vec(A'B') = sqrt((-1-7)^2 + (15-3)^2) = 14.42 " units"#

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