A line segment has endpoints at #(1 ,4 )# and #(7 ,3 )#. The line segment is dilated by a factor of #3 # around #(2 ,6 )#. What are the new endpoints and length of the line segment?

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Answer 1 · 2018-02-20T08:38:04

New end points #A’((-1),(0))#, #B’((17),(-3))#

Length of line segment after dilation

#vec(A’B’) = 16.2788#

#A (1,4), B (7,3)#, dilated around #C (2,6)# and dilation factor 3

#A’ = 3A - 2C = 3((1),(4)) - 2((2),(6)) = ((3),(12)) - ((4),(12)) = ((-1),(0))#

#B’ = 3B - 2C = 3((7),(3)) - 2((2),(6)) = ((21),(9)) - ((4),(12)) = ((17),(-3))#

Length of line segment after dilation

#vec(A’B’) = sqrt((17+1)^2 + (-3-0)^2) = 16.2788#