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Math Help - equation to represent locus of points equidistant from 2 other equations

  1. #1
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    equation to represent locus of points equidistant from 2 other equations

    i know how to do it if the question was "determine equation of locus of points equidistant from 2 other POINTS" (use distance formula and square both sides, etc), but not 2 other EQUATIONS.

    so for example, y=x and y=-x

    how do you find equation of locus equidsitant from those 2 lines?
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  2. #2
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    locus points equidistantfrom two lines

    Hi iragequit,
    Your example defines two lines perpendicular to each other.The locus of points equidistant to them are the x and y axis.For a general case of two intersecting lines the locus is the angle bisector between them.


    bjh
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    Quote Originally Posted by bjhopper View Post
    Hi iragequit,
    Your example defines two lines perpendicular to each other.The locus of points equidistant to them are the x and y axis.For a general case of two intersecting lines the locus is the angle bisector between them.


    bjh
    the answer in the back says its xy=0 o_o

    and i don't understand this term "angle bisector".

    could you do a specific example with 2 lines or something (i don't know why they don't do examples of this in my book but give questions on it.. can't find it on google either)? and they don't have to be intersecting as far as i know
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  4. #4
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    First, let me point out that "equations" are not geometric objects so it makes no sense to talk about "the locus of points equidistant from two equations". You mean, as bjhopper said, the locus of point equidistant from the two lines defined by those equations.

    An "angle bisector" is the line or ray that divides an angle into two equal parts. Actually when two lines intersect, they divide the plane into four parts so there are four angles. The locus you seek is the pair of lines that divide those four angles into equal parts. The lines defined by y= x and y= -x are at right angles to one another so the lines that bisect them are at 45 degrees to them. Those are, again as bjhopper said, the x and y axes.
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    Quote Originally Posted by HallsofIvy View Post
    First, let me point out that "equations" are not geometric objects so it makes no sense to talk about "the locus of points equidistant from two equations". You mean, as bjhopper said, the locus of point equidistant from the two lines defined by those equations.

    An "angle bisector" is the line or ray that divides an angle into two equal parts. Actually when two lines intersect, they divide the plane into four parts so there are four angles. The locus you seek is the pair of lines that divide those four angles into equal parts. The lines defined by y= x and y= -x are at right angles to one another so the lines that bisect them are at 45 degrees to them. Those are, again as bjhopper said, the x and y axes.
    how do i find the angle bisector algebraically of complicated equations?
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  6. #6
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    Hi iragequit,
    Post one of the bisector problems in your book.


    bjh
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