Constructible line
= Constructible line
A <constructible line> is a <line> through two distinct <constructible points>. If the available coordinates lie in a real <field> $F$, a <line> through $(a,b)$ and $(c,d)$ has equation $(d-b)(x-a)-(c-a)(y-b)=0$, with <coefficients> in $F$ and a nonzero <normal vector>. Intersecting two distinct such <lines> introduces no new <field> elements, because solving a nonsingular pair of <linear equations> uses only <field> operations.