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Math Help - Locus question #1

  1. #1
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    Red face Locus question #1

    My question is:

    Find the equation of the locus of a point P(x,y) that moves so that it is equidistant from the x-axis and the y-axis, please tell me step by step all the working out please
    Last edited by mr fantastic; August 1st 2010 at 12:57 AM. Reason: Title.
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  2. #2
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    Quote Originally Posted by moeyfrompunchy View Post
    My question is:

    Find the equation of the locus of a point P(x,y) that moves so that it is equidistant from the x-axis and the y-axis, please tell me step by step all the working out please
    In order for point P to be equidistant from the x and y-axis, it has to move along the line y=x.
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  3. #3
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    Hello, moeyfrompunchy!

    Did you even bother to make a sketch?


    Find the equation of the locus of a point P(x,y)
    that moves so that it is equidistant from the x-axis and the y-axis.
    Code:
          |         P
        B + - - - - *(x,y)
          |    x    :
          |         :
          |         : y
          |         :
          |         :
      ----+---------+----
          |         A
          |

    The point is P(x,y).

    Its distance from the x-axis is: . PA = y.

    Its distance from the y-axis is: . PB = x.

    We want these distances to be equal: . y \:=\:x



    How hard was that?
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  4. #4
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    Quote Originally Posted by moeyfrompunchy View Post
    My question is:

    Find the equation of the locus of a point P(x,y) that moves so that it is equidistant from the x-axis and the y-axis, please tell me step by step all the working out please
    1. If the point P has equal distances from the axes then you have:

    |y| = |x|

    2. If you write this equation without the absolute values you'll get as the locus l:

    l: y = x~\vee~y = -x
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