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Linear Transformation: Finding the Transformation of a Line

  1. Mar 30, 2012 #1
    Having a bit of trouble with this one. Can anyone help?

    Many thanks.

    1. The problem statement, all variables and given/known data

    Q. L is the line x - y + 1 = 0. f is the transformation f: (x, y) ---> (x', y') where: x' = 2x - y & y' = y. Find f(L) and investigate if f(L) is parallel to L.

    2. Relevant equations


    3. The attempt at a solution

    If y = y', then x' = 2x - y => 2x = x' - y => 2x = x' - y' => x = [itex]\frac{x' - y'}{2}[/itex]

    If L = x - y + 1 = 0, then f(L) = [itex]\frac{x' - y'}{2}[/itex] - y' + 1 = 0 => x' - y' - 2y' + 2 = 0 => x' - 3y' + 2 = 0

    Now apply x/ y values to f(L) = x' - 3y' + 2 = 0 => 2x - y - 3y + 2 = 0 => 2x - 4y + 2 = 0 => x - 2y + 1 = 0 => 2y = x + 1 => y = [itex]\frac{x - 1}{2}[/itex]

    Ans: (From text book): y = x + 2
     
  2. jcsd
  3. Mar 30, 2012 #2

    Dick

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    Science Advisor
    Homework Helper

    You went off course on the first line. If x'=2x-y' then 2x=x'+y'.
     
  4. Mar 30, 2012 #3
    Great, thank you.
     
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