A line segment has endpoints at #(1 ,2 )# and #(3 , 1)#. The line segment is dilated by a factor of #4 # around #(2 , 5)#. What are the new endpoints and length of the line segment?

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Answer 1 · 2018-02-05T08:41:32

New end points #color(brown)((-2, -7)# & #color(brown)((6, -11)#

Length of the line segment #color(green)(d ~~ 8.94)#

Given : End points A(1,2), B (3,1), Center of dilation C(2,5) and dilation factor 4

Let A' and B' be the new end points after dilation.

#bar(CA') = 4 * bar(CA)#

#a' - c = 4 * (a - c)#

#a' = 4a - 3c#

#=>4((1),(2)) -3((2),(5))#

#=>((4),(8)) - ((6),(15)) = ((-2),(-7))#

#color(brown)(A' (-2, -7)#

#bar(CB') = 4 * bar(CB)#

#b' - c = 4(b-c)#

#b' = 4b - 3c#

#=> 4 ((3),(1)) - 3((2),(5))#

#=>((12),(4)) - ((6),(15)) = ((6),(-11))#

#color(brown)(B' (6, -11)#

Using distance formula we can find the length A'B'

#bar(A'B') = sqrt((6-(-2))^2 + ((-11) - (-7))^2) = sqrt(8^2 + 4^2) ~~ color(green)(8.94# corrected to two decimal points