A line segment has endpoints at #(0 ,9 )# and #(8 ,2 )#. The line segment is dilated by a factor of #2 # around #(1 ,1 )#. What are the new endpoints and length of the line segment?

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Answer 1 · 2018-02-12T11:31:15

New end points #color(purple)(((-1),(17)),((15),(3))#

Length of the line segment #~~ color(green)(21.26)#

#A ((0),(9)), B ((8),(2)), C ((1),(1))# Dilation factor around C is 2

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

#a' = 2 ((0),(9)) - ((1),(1)) = ((-1),(17))#

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

#b' = 2((8),(2)) - ((1),(1)) = ((15),(3))#

#vec(A'B') = sqrt((15+1)^2 + (3-17)^2) ~~ color(green)(21.26)#