A line segment has endpoints at #(2 ,1 )# and #(6 ,2 )#. 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 · 2018-02-10T09:02:22

New end points coordinates of #A ((2),(1)), B ((18),(5))#

length of line segment #~~ color(green)(16.49#

Given : A(2,1), B(6,2), 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((2),(1)) - 3 ((2),(1)) = ((8),(4)) - ((6),(3)) = color(brown)(((2),(1))#

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

#b' = 4((6),(2)) - 3 ((2),(1)) = ((24),(8)) - ((6),(3)) = color(brown)( ((18),(5))#

Length of the line segment using distance formula,

#vec(A'B') = sqrt((2-18)^2 + (1-5)^2) ~~ color(green)(16.49#