Show that, given two distinct points (s, t) and (u, v) of this geometry, the unique line incident with these two points can be parameterized as follows: I {} = Au + (1-X)s, y = Av + (1-X)t, XEQ. (Hint. First use point-slope form to find a corresponding equation for the line. Then show that any point of the parameterization satisfies the given equation. You can use the fact that Q is closed under addition and multiplication; that means that, for any two rational numbers, their sum and product is still rational. Lastly, show that any point on the line has a corresponding A for which it is parameterized accordingly. To do this, simply solve one of the expressions for A based on your given values and demonstrate that A must be rational. Then show that the given A produces the desired point.) (This allows us to see the betweenness relation in terms of the real line R.) Show that this structure satisfies the axiom B2.

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