# Find third point in mapping system

I have two points defined: $A$ and $B$

For both I know $x,y$, longitude, and latitude (gps coordinates). How do I calculate $x,y$ of a third point $C$ when I know its longitude and latitude?

I know this is very basic but I cannot get my head around it at the moment.

Edit: I want a basic math proportion calculation, without taking into consideration Earth's surface and how coordinates is calculated.

Edit: I think I figured it out. (Can't answer my own question yet) for $x$: $$\frac{|lon_A-lon_B|}{|lon_C-lon_A|} = \frac{|x_A-x_B|}{|x_C-x_A|}$$

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I think the question as stated doesn't make sense. Somewhere behind the question there's a function from the Earth's surface to a Cartesian co-ordinate system, but if all we know about that function is two of its values, there's no way to calculate a third value. It's a little like asking, find the third number in the sequence 4, 8, x. Unless you know something about the rule behind the scenes, there's not much you can say. –  Gerry Myerson Jun 22 '11 at 0:29
I am new here, also considerably new to latex. Can anybody fix the equation in the question? I think it validates in latex but does not show here. –  rok Jun 22 '11 at 0:50
@rok: I hope that's what you wanted. You need to use only a $ at the beginning of a formula and at the very end of it, so e.g. $\frac{x_1}{y_1} = 2^3$ gives$\displaystyle\frac{x_1}{y_1} = 2^3$– t.b. Jun 22 '11 at 0:58 @rok, if all you want is a proportion calculation, then you've done it correctly. And I think you can see how to do it for$y\$ as well. –  Gerry Myerson Jun 22 '11 at 1:17
This is valid in a small region. Particularly if the latitude covers a wide range, this will not be accurate as the circumference of the earth varies with latitude. Wide range of longitude is not a problem. –  Ross Millikan Jun 22 '11 at 3:28

This isn't an answer but I found your question interesting and wanted to share some of my ideas.

There are many different projections from the earth to an x-y plane. See: http://en.wikipedia.org/wiki/Map_projection. So my first suggestion, if you know or can guess the 'center' of the projection, would be to try plugging the points you have into some of the equations given for some common projections (these can be found on their respective wiki pages). Alternatively, if you know the type of projection you could derive the center easily and that would solve your problem.

If you wanted to try to derive the projection yourself, you need at least 3 non-collinear points to describe the projected plane. From there you could try experimenting with different functions to see if one gives a good fit.

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thanks for the suggestion, I'll look into this. The problem is I have a map for a very small region (city, town) so how can I guess the 'center'? –  rok Jun 24 '11 at 14:46