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Homework Help: Finding co-ordinate

  1. Sep 22, 2010 #1
    1. The problem statement, all variables and given/known data

    find the set of all points (x,y) which satisfy lxl + lyl = 1

    2. Relevant equations



    3. The attempt at a solution

    first i decided to make lxl and lyl into inequality.

    -1 < x < 1
    -1 < y < 1

    lxl = lyl - 1

    so from any value of y between (-1,1) would work ? will this give lxl the correct result?
    will they both equal to 1 ?
    please help im confused.
     
  2. jcsd
  3. Sep 23, 2010 #2

    Mentallic

    User Avatar
    Homework Helper

    There are 4 cases to consider:

    x,y>0
    x>0, y<0
    x<0, y>0
    x,y<0

    For the first, obviously you have the line y=1-x. And yes you place the restrictions that [itex]0\leq x\leq 1[/itex]. Can you finish the rest?
     
  4. Sep 23, 2010 #3
    hm... logically wouldnt y = 1 - x be the only solution ? since we are not dealing with absolute values anymore.

    or should i keep absolute values in the calculations?

    lyl = 1 - lxl

    -1 < x < 0
     
  5. Sep 23, 2010 #4

    Mentallic

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    Homework Helper

    Well that's like saying logically shouldn't x=1 be the only solution to |x|=1.

    The point (-1/2, 1/2) satisfies the equation, but this point doesn't lie on the line y=1-x. Try do what I suggested in my previous post.
     
  6. Sep 23, 2010 #5

    Mark44

    Staff: Mentor

    Is this exactly how the problem is stated?

    A reasonable, but not very helpful, answer is {(x, y) | |x| + |y| = 1}. Another reasonable answer is a graph of this equation.
     
  7. Sep 24, 2010 #6

    The question asks to graph for all coordinates (x,y) which satisfy l x l + l y l = 1
     
  8. Sep 24, 2010 #7

    Mark44

    Staff: Mentor

    OK, that makes more sense. Follow Mentallic's advice in post #2.
     
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