A line segment has endpoints at #(1 ,4 )# and #(5 ,3 )#. 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 · 2018-02-05T11:43:53

New end points #color(purple)(A' (-1,0)#, #color(purple)(B' (11,-3)#

Length of the line segment after dilation is

#vec(A'B') ~~ color(green)(12.37)# rounded to 2 decimals

Given : A(1,4), B(5,3), Dilated around C(2,6), dilation factor 3

To find the new end points and length of line segment.

#vec(A'C) = 3 * vec(AC)# or #a' = 3a - 2c#

#a' = 3 ((1),(4)) - 2 ((2),(6)) = ((3),(12)) - ((4),(12)) = color(purple)(((-1),(0))#

#vec(B'C) = 3 * vec(BC)# or #b' = 3b - 2c#

#b' = 3 ((5),(3)) - 2 ((2),(6)) = ((15),(9)) - ((4),(12)) = color(purple)(((11),(-3))#

#vec(A'B') = sqrt((-1-11)^2 + (0-(-3))^2) ~~ color(green)(12.37)# rounded to 2 decimals