A line segment has endpoints at #(5 ,9 )# and #(2 ,2 )#. The line segment is dilated by a factor of #2 # around #(5 ,3 )#. What are the new endpoints and length of the line segment?

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Answer 1 · 2018-06-08T01:36:36

#color(maroon)("New endpoints are" A' (5,21), B' (-4,0)#

#color(blue)("Length of the line segment "bar(A'B') = 15,23#

#A (5,9), B (2,2), C (5,3), " dilation factor " 2#

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

#A'((x),(y)) = 2((5),(9)) - ((5),(3)) = ((5),(15))#

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

#B'((x),(y)) = 2((2),(2)) - ((5),(3)) = ((-1),(1))#

Length of the line segment

#bar(A'B') = sqrt((5+1)^2 + 14^2) = 15.23#