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

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Answer 1 · 2018-03-03T02:05:13

New endpoints #color(red)(A’ (8,4), B’(4,12)#

Length of the new line segment #color(purple)(vec(A’B’) ~~ 8.9443#

Given #A (3,2), B (2,4)# Rotated about #C(1,1)# by a factor of 4.

To find the new endpoints and the length of the line segment.

#vec(A’C) = 4 * vec(AB)#

#a’((x),(y)) -=c((1),(1)) = 4 * ((3),(2)) - 4 * ((1),(1))#

#a’((x),(y)) = 4 * ((3),(2)) - 3 * ((1),(1)) = ((12),(8)) - ((4),(4)) = ((8),(4))#

Similarly,

#b’((x),(y)) = = 4 * ((2),(4)) - 3 * ((1),(1)) = ((8),(16)) - ((4),(4)) = ((4),(12))#

Length of the new line segment

#vec(A’B’) = sqrt((4-8)^2 + (4-12)^2) ~~ color (purple)(8.9443#