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

  • Thread starter Denyven
  • Start date
19
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1. Homework Statement
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. Homework 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!
 

Answers and Replies

152
0
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.
 
tiny-tim
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Homework Helper
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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:
 
19
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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:
tiny-tim
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Homework Helper
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Tiny Tim,
What do you mean convert y1+y2 into x1+x2?
No, I said x1 and x2.
… 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?
What on earth are you doing?

What happened to x1 and x2? :confused:

Put them back!!
 
19
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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?
 
tiny-tim
Science Advisor
Homework Helper
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No, I mean y1 = 4x12 + 7x1 - 1

and y2 = 4x22 + 7x2 - 1
 

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