A line segment has endpoints at #(3 ,5 )# and #(6 ,1 )#. The line segment is dilated by a factor of #4 # around #(1 ,3 )#. What are the new endpoints and length of the line segment?

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Answer 1 · 2018-06-19T04:36:30

#color(indigo)(bar(A'B') = sqrt((9-21)^2 + (11+5)^2) = 20#

#A (3,5), B (6,1), C (1,3), " dilation factor " 4#

#A'C = 4 (a - c)#, #A' - c = 4a - 3c#

#A'((x),(y)) = 4((3),(5)) - 3((1),(3)) = ((9),(11))#

#B'C = 4 (b - c)#, #B' - c = 4b - 3c#

#B'((x),(y)) = 4((6),(1)) - 3((1),(3)) = ((21),(-5))#

Length of the line segment

#color(indigo)(bar(A'B') = sqrt((9-21)^2 + (11+5)^2) = 20#