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Two points on a graph, the mid-point of a line made by these two points is an origin.

  1. Nov 22, 2009 #1
    1. The problem statement, all variables and given/known data
    Two points are located on the graph [tex]y=4x^{2}+7x-1[/tex]. A line drawn between these two points have a mid-point at (0,0). Find these two points.


    2. Relevant equations
    The midpoint formula [tex](x_{m},y_{m})=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]


    3. The attempt at a solution
    I have worked out the distance from a point on the graph to the origin as a function of x [tex]d=\sqrt{16x^{4}+56x^{3}+42x^{2}-14x+1}[/tex], by plugging in the parabolic equation into the [tex]d=\sqrt{x^{2}+y^{2}}[/tex]. I have also figured out these set of rules for [tex]x_{1}, x_{2}, y_{1}[/tex] and [tex]y_{2}[/tex]:
    [tex]x_{1}+x_{2}=0[/tex] and [tex]y_{1}+y_{2}=0[/tex]
    Thus [Tex]x_{1}= -x_{2}[/tex] and [tex]y_{1}= -y_{2}[/Tex]
    All of the above were derived from the midpoint formula, since the mid-point is (0,0), both the x's and the y's have to cancel out each other.

    Thanks in Advance!
     
  2. jcsd
  3. Nov 22, 2009 #2
    Re: Two points on a graph, the mid-point of a line made by these two points is an ori

    This is interesting, i dont think its possible to find the where these points are located without any information about where at least one of them is.

    but i may just not be looking close enough for a solution.
     
  4. Nov 22, 2009 #3

    tiny-tim

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    Hi Denyven! :wink:

    ok, so y1 + y2 = 0.

    Now convert that equation into x1 and x2.

    What do you get? :smile:
     
  5. Nov 22, 2009 #4
    Re: Two points on a graph, the mid-point of a line made by these two points is an ori

    Tiny Tim,
    What do you mean convert y1+y2 into x1+x2?
    Like this [tex]x_{1}+x_{2}=y_{1}+y_{2}[/tex]
    Or plug the equation of a parabola into the y1+y2?
    Which would yield [tex]y=8x^{2}+14x-2[/tex], who's zeros are [tex]x=\frac{1}{8}(-7-\sqrt{65})[/tex] and [tex]x=\frac{1}{8}(\sqrt{65}-7)[/tex].
    Are these the x values of either points?
     
    Last edited: Nov 22, 2009
  6. Nov 22, 2009 #5

    tiny-tim

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    No, I said x1 and x2.
    What on earth are you doing?

    What happened to x1 and x2? :confused:

    Put them back!!
     
  7. Nov 22, 2009 #6
    Re: Two points on a graph, the mid-point of a line made by these two points is an ori

    oh ha,
    so do you mean x1=y1+y2-x2 and x2=y1+y2-x1?
     
  8. Nov 22, 2009 #7

    tiny-tim

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    No, I mean y1 = 4x12 + 7x1 - 1

    and y2 = 4x22 + 7x2 - 1
     
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