$33\mathrm{.}2-2$

Given two segments a and $b$ that are comparable at $x,$ show how to determine

in $O(1)$ time which of $a{}_{x}b$ or $b{}_x$a holds. Assume that neither segment

is vertical. $($Hint: If a and $b$ do not intersect, you can just use cross products.

If a and $b$ intersect$-$which you can of course determine using only cross prod$-$

ucts$-$you can still use only addition, subtraction, and multiplication, avoiding

division. Of course, in the application of the ${}_x$ relation used here, if a and $b$

intersect, we can just stop and declare that we have found an intersection.$)$