A line segment has endpoints at #(5 ,1 )# and #(3 ,9 )#. The line segment is dilated by a factor of #5 # around #(2 ,2 )#. What are the new endpoints and length of the line segment?

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Answer 1 · 2018-02-05T11:33:25

New end points #A' color(brown)( ((17,-3)), # #B' color(brown)((7,37)#

Length of the line segment #vec(A'B') ~~ color(green)(41.23#

Given : A(5,1), B(3,9), dilated around C (2,2) & dilation factor 5

To find : End points and length of line segment after dilation

#vec(A'C) = 5 * vec(AC)# or #a' = 5a - 4c#

#a' = 5((5),(1)) - 4((2),(2)) = ((25),(5)) - ((8),(8)) =color(brown)( ((17),(-3))#

#vec(B'C) = 5 * vec(BC)# or #b' = 5b - 4c#

#b' = 5((3),(9)) - 4((2),(2)) = ((15),(45)) - ((8),(8)) = color(brown)( ((7),(37))#

#vec(A'B') = sqrt((17-7)^2 + (-3 -37)^2) ~~ color(green)(41.23#