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

1. Nov 22, 2009

### Denyven

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

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

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 $$d=\sqrt{16x^{4}+56x^{3}+42x^{2}-14x+1}$$, by plugging in the parabolic equation into the $$d=\sqrt{x^{2}+y^{2}}$$. I have also figured out these set of rules for $$x_{1}, x_{2}, y_{1}$$ and $$y_{2}$$:
$$x_{1}+x_{2}=0$$ and $$y_{1}+y_{2}=0$$
Thus [Tex]x_{1}= -x_{2}[/tex] and $$y_{1}= -y_{2}[/Tex] All of the above were derived from the midpoint formula, since the mid-point is (0,0), both the x's and the y's have to cancel out each other. Thanks in Advance! 2. Nov 22, 2009 ### um0123 Re: Two points on a graph, the mid-point of a line made by these two points is an ori This is interesting, i dont think its possible to find the where these points are located without any information about where at least one of them is. but i may just not be looking close enough for a solution. 3. Nov 22, 2009 ### tiny-tim Hi Denyven! ok, so y1 + y2 = 0. Now convert that equation into x1 and x2. What do you get? 4. Nov 22, 2009 ### Denyven Re: Two points on a graph, the mid-point of a line made by these two points is an ori Tiny Tim, What do you mean convert y1+y2 into x1+x2? Like this [tex]x_{1}+x_{2}=y_{1}+y_{2}$$
Or plug the equation of a parabola into the y1+y2?
Which would yield $$y=8x^{2}+14x-2$$, who's zeros are $$x=\frac{1}{8}(-7-\sqrt{65})$$ and $$x=\frac{1}{8}(\sqrt{65}-7)$$.
Are these the x values of either points?

Last edited: Nov 22, 2009
5. Nov 22, 2009

### tiny-tim

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

What happened to x1 and x2?

Put them back!!

6. Nov 22, 2009

### Denyven

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?

7. Nov 22, 2009

### tiny-tim

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

and y2 = 4x22 + 7x2 - 1

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