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