A line segment has endpoints at #(3 ,8 )# and #(3 , 9)#. The line segment is dilated by a factor of #3 # around #(2 , 3)#. What are the new endpoints and length of the line segment?

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Answer 1 · 2018-06-07T13:58:44

New end points are #(5,18) & (5,21)#

Length of the line segment after dilation is #3#

#A(3,8), B(3,9), C(2,3)#, dilation factor #3#

#A’ = 3a - 2c#

#A’((x),(y)) = 3 * ((3),(8)) - 2 * ((2),(3))#

#A’((x),(y)) = ((5),(18))#

#B’((x),(y)) = 3 * ((3),(9)) - 2 * ((2),(3))#

#B’((x),(y)) = ((5),(21))#

Length of the line segment after dilation

#vec(A’B’) = sqrt((5-5)^2 + (21-18)^2) = 3#