A line segment has endpoints at #(7 ,2 )# and #(3 ,4 )#. The line segment is dilated by a factor of #6 # around #(4 ,5 )#. What are the new endpoints and length of the line segment?

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Answer 1 · 2018-06-19T04:45:05

#color(maroon)(bar(A'B') = sqrt((22+2)^2 + (-13+1)^2) = 26.83#

#A (7,2), B (3,4), C (4,5), " dilation factor " 6#

#A'C = 6 (a - c)#, #A' - c = 6a - 5c#

#A'((x),(y)) = 6((7),(2)) - 5((4),(5)) = ((22),(-13))#

#B'C = 6 (b - c)#, #B' - c = 6b - 5c#

#B'((x),(y)) = 6((3),(4)) - 5((4),(5)) = ((-2),(-1))#

Length of the line segment

#color(maroon)(bar(A'B') = sqrt((22+2)^2 + (-13+1)^2) = 26.83#