Results 1 to 2 of 2

Math Help - Cartesian Plane

  1. #1
    Junior Member
    Joined
    Feb 2008
    Posts
    49

    Cartesian Plane

    Find an equation of the set of points in the Cartesian plane that are equidistant from the point (-1,1) and the line y=x.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,546
    Thanks
    539
    Hello, chaddy!

    Find an equation of the set of points in the Cartesian plane
    that are equidistant from the point (-1,1) and the line y=x.
    Code:
                  |
                  | P
                  | *(x,y)      *
                  /  \        *
             A  / |   \     *
              *   |    \  *
           (-1,1) |     *
                  |   *  B
                  | *
          - - - - * - - - - - - - -
                * |
              *   |

    The distance from point P(x,y) to point A(-1,1)

    . . is given by: . PA \;=\;\sqrt{(x+1)^2 + (y-1)^2}



    The distance from a point P(x_1,y_1) to a line ax + by + c\:=\:0

    . . is given by: . d \;=\;\frac{|ax_1 + by_1 + c|}{\sqrt{a^2+b^2}}

    Hence, the distance from P(x,y) to the line x - y \:=\:0

    . . is given by: . PA \;=\;\frac{|x-y|}{\sqrt{1^2 + (-1)^2}} \;=-\;\frac{|x-y|}{\sqrt{2}}


    Since PA = PB, we have: . \sqrt{(x+1)^2 + (y-1)^2} \;=\;\frac{|x-y|}{\sqrt{2}}


    Now simplify . . .

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Cartesian plane
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: July 20th 2010, 11:25 PM
  2. cartesian plane....
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: September 28th 2009, 08:27 AM
  3. Cartesian eqn of a plane
    Posted in the Geometry Forum
    Replies: 2
    Last Post: June 21st 2009, 02:57 PM
  4. cartesian plane
    Posted in the Geometry Forum
    Replies: 2
    Last Post: November 17th 2008, 05:29 AM
  5. cartesian plane
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 14th 2008, 05:48 AM

Search Tags


/mathhelpforum @mathhelpforum