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Homework Help: Straight lines questions.

  1. Jan 22, 2012 #1
    1. The problem statement, all variables and given/known data
    If the distance of any point (x,y) from the origin is defined as
    d (x, y) = max {|x|,|y|},
    d (x, y) = a non zero constant, then the locus is

    (a) a circle
    (b) a straight line
    (c) a square
    (d) a triangle

    2. Relevant equations

    3. The attempt at a solution
    I don't understand what does the question mean by "d (x, y) = max {|x|,|y|}"?

    Can somebody tell what does the notation mean? I never encountered problems like these.
    Any help is much appreciated.

    Thanks! :smile:
  2. jcsd
  3. Jan 22, 2012 #2


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    what do you understand of the various symbols used?

    What does "|x|" mean, for example

    If you have no idea what the symbols mean, one has to wonder what you are doing working on the problem with no background, but if you do understand them, then say what they are and see where that leads.
  4. Jan 22, 2012 #3
    I know what does |x| mean. My question is what does this "max" and "d(x,y)" mean?
    (x,y) are the co-ordinates of a point but i don't understand what this "d(x,y)" mean.

    Thanks for the reply! :smile:
  5. Jan 22, 2012 #4


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    d(x,y) is just a function, it is not the same as the classical distance. It is defined as max(|x|,|y|), so d=|x| when |x|>|y| and d=|y| when |y|>|x|. Find the locus where d(x,y)= constant. Draw a picture of the coordinate system and find the regions where |y|>|x| and |x|>|y|. Draw the lines d=const. You will see the solution at once.

  6. Jan 22, 2012 #5
    I drew the graph of the both |x| and |y| on the same graph and found that the graphs of both |x| and |y| coincides with each other.
    Is the coinciding line is my answer?
  7. Jan 22, 2012 #6


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    NO. Show your drawing, please. You need to find those points in that domain of the x,y plane where |y|>|x| for which d(x,y)= |y| =const, for example d(x,y) = |y|=5. And also find those points (x,y), |x|>|y|, for which d(x,y)=|x|=5

  8. Jan 22, 2012 #7
    My graph is similar to this:- http://www.wolframalpha.com/input/?i=|y|=x,y=|x|
  9. Jan 22, 2012 #8


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    The plot is a good start to show the domains, but complete it for x<0, y<0. Then draw the line(s) |y|=5 in the range |x|<|y|.

    Last edited: Jan 22, 2012
  10. Jan 22, 2012 #9
    Here's the graph which i drew (Not to scale):-

    |y|=5, that mean y=5 or y=-5, i draw both of them but i still don't understand what you mean by |x|<|y|?

    Sorry if this is annoying for you.
  11. Jan 22, 2012 #10


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    The lines y=5 and y=-5 do not extend to infinity. d(x,y)=max(|x|,|y|)=5. It is equal to |y| while |y|>|x|, in the yellow area of the x,y plane. In the blue area, where |x|>|y|, d(x,y)=5=|x|. Draw it.


    Attached Files:

  12. Jan 22, 2012 #11

    I like Serena

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    Homework Helper

    Hi Pranav! :smile:

    Perhaps you could consider a few points in the plane.
    Like (x=1, y=5), (-4,5), (-6,5), (1,1), (-5,4), (-5,-4), (-3,-5).
    Can you say what max(|x|,|y|) is in each case?
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