A line segment has endpoints at #(1 ,4 )# and #(7 ,9 )#. The line segment is dilated by a factor of #3 # around #(2 ,6 )#. What are the new endpoints and length of the line segment?

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Answer 1 · 2018-06-19T04:40:53

#color(brown)(bar(A'B') = sqrt((-1-17)^2 + (0-15)^2) = 23.43#

#A (1,4), B (7,9), C (2,6), " dilation factor " 3#

#A'C = 3 (a - c)#, #A' - c = 3a - 2c#

#A'((x),(y)) = 3((1),(4)) - 2((2),(6)) = ((-1),(0))#

#B'C = 3 (b - c)#, #B' - c = 3b - 2c#

#B'((x),(y)) = 3((7),(9)) - 2((2),(6)) = ((17),(15))#

Length of the line segment

#color(brown)(bar(A'B') = sqrt((-1-17)^2 + (0-15)^2) = 23.43#