A line segment has endpoints at #(1 ,6 )# and #(5 ,8 )#. The line segment is dilated by a factor of #4 # around #(2 ,1 )#. What are the new endpoints and length of the line segment?

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Answer 1 · 2018-02-10T09:09:16

New end points #A' ((-2),(21)), B'((14),(29))#

Line segment length #~~ color(green)(28.64#

Given : A(1,6), B(5,8), dilated around C(2,1), dilation factor 4

To find the end points of the line segment and its length

#vec(A'C) = 4 * vec(AC)# or #a' = 4a - 3c#

#a' = 4((1),(6)) - 3 ((2),(1)) = ((4),(24)) - ((6),(3)) = color(brown)(((-2),(21))#

#vec(B'C) = 4 * vec(BC)# or #b' = 4b - 3c#

#b' = 4((5),(8)) - 3 ((2),(1)) = ((20),(32)) - ((6),(3)) = color(brown)( ((14),(29))#

Length of the line segment using distance formula,

#vec(A'B') = sqrt((-2-14)^2 + (3-29)^2) ~~ color(green)(28.64#