A line segment has endpoints at #(9 ,3 )# and #(5 ,9 )#. The line segment is dilated by a factor of #3 # around #(4 ,4 )#. What are the new endpoints and length of the line segment?

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Answer 1 · 2018-07-27T05:52:43

#color(brown)(A' (19,1), B' (7,18)#

#color(chocolate)("Length of the line segment after dilation "color(blue)(vec(A’B’) ~~ 21.6333#

#A(9, 3), B(5, 9), C(64, 4)#, dilation factor #3#

#A’ = 3a - 2c#

#A’((x),(y)) = 3 * ((9),(3)) - 2 * ((4),(4))#

#A’((x),(y)) = ((19),(1))#

#B’((x),(y)) = 3 * ((5),(9)) - 2 * ((4),(4))#

#B’((x),(y)) = ((7),(19))#

#color(brown)("Length of the line segment after dilation "#

#color(blue)(vec(A’B’) = sqrt((19- 7)^2 + (1- 19)^2) ~~ 21.6333#