A line segment has endpoints at #(2 ,8 )# and #(2 , 1)#. The line segment is dilated by a factor of #3 # around #(6 , 4)#. What are the new endpoints and length of the line segment?

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Answer 1 · 2018-02-05T12:02:24

Two end points are #A' = color(brown)(-6, 16)#, #B' = = color(brown)(-6, -5)#

Length of the line segment using distance formula,#vec(A'B') = color(green)(21#

Given : A(2,8), B(2,1), dilated around C(6,4), dilation factor 3

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

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

#a' = 3((2),(8)) - 2 ((6),(4)) = ((6),(24)) - ((12),(8)) = color(brown)(((-6),(16))#

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

#a' = 3((2),(1)) - 2 ((6),(4)) = ((6),(3)) - ((12),(8)) = color(brown)( ((-6),(-5))#

Length of the line segment using distance formula,

#vec(A'B') = sqrt((-6+6)^2 + (16+5)^2) = color(green)(21#