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

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Answer 1 · 2018-02-12T11:22:20

New coordinates of end points #color(purple)(((6),(-1)), ((2),(11))#

Length of the line segment #vec(A'B') = ~~ color(green)(12.65#

Existing points A (3,2), B (2,5). Dilated around C (2,3) by factor 4

To find new end points and length of segment.

#vec(A'C) = 4 * vec(AC) or a' = 4a - 3c#

#a' = 4 ((3),(2)) - 3 ((2),(3)) = ((12),(8)) - ((6),(9)) => ((6),(-1))#

#vec(B'C) = 4 (vec(BC)) or b' = 4a - 3c #

#b' = 4((2),(5)) - 3 ((2),(3)) = ((8),(20)) - ((6),(9)) = ((2),(11))#

#vec(A'B') = sqrt((2-6)^2 + (11+1)^) = sqrt160 ~~ color(green)(12.65#