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Math Help - Coordinate Geometry

  1. #1
    Newbie Ai Ekio's Avatar
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    Coordinate Geometry

    The directions say I'm supposed to sketch each locus on a coordinate plane..so graph paper..
    1. All points 3 units from line y=-2
    2. All points equidistant from points (2,4) and (0,0)

    I'm clueless as to what the resulting sketches are supposed to look like..where is 'line y=-2" on the coordinate plane anyway?Please help,I'm totally confused.Thank you..
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  2. #2
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    Quote Originally Posted by Ai Ekio View Post
    The directions say I'm supposed to sketch each locus on a coordinate plane..so graph paper..
    1. All points 3 units from line y=-2
    All the points 3 units from the line y = - 2 lie on a line which is 3 units from the given line. So, the locus is the line y = 1 and line y = - 5

    please see attached graph.
    Attached Thumbnails Attached Thumbnails Coordinate Geometry-graph36.jpg  
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  3. #3
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    Quote Originally Posted by Ai Ekio View Post
    The directions say I'm supposed to sketch each locus on a coordinate plane..so graph paper..
    2. All points equidistant from points (2,4) and (0,0)
    The locus of the points equi-distant from these points, is the line which is perpendicular bisector of the line joining these two given points.

    The midpoint between the points (2, 4) and (0,0) is \left(\frac{2+0}{2}, \frac{4+0}{2}\right)=(1, 2)

    Slope =\frac{4-0}{2-0}=2

    Slope of perpendicular line = \frac{-1}{2}

    Equation of locus line (pink line in the graph) is

    y = \frac{-1}{2}x+b

    2 = \frac{-1}{2}(1)+b

    b = \frac{5}{2}

    equation of locus line is

    y = \frac{-1}{2}x+\frac{5}{2}

    x + 2y = 5
    Attached Thumbnails Attached Thumbnails Coordinate Geometry-graph37.jpg  
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