% Plane-geometry problems

Plane geometry
--------------
Here are a bunch of problems with eventual applications to
**map-drawing** and **visualization of geographic data**.


Two points $A$ and $B$ define a line.  Compute the directed distance
from that line to a third point $C$. There are many ways to solve this problem.

  - The most satisfying solution involves drawing a line parallel to $AB$
    through point $C$ and then looking at the triangles and the
    angles.  You can bring some trigonometry into play.

  - The lazy person's solution is to look for the MathWorld article on
    the area of the triangle $ABC$ and then to realize that the area
    of a triangle is half the length of the base $AB$ multiplied by
    the distance from the base to the point $C$.

Computations involving trigonometric functions or square roots involve
*inexact* numbers.  You will want to write test cases using
`check-within`.



Given a set of points in the plane, find the closest point to a query
using linear search (requires lists)

Given a set of points in the plane, find the closet point to a query
using generative recursion in the form of a kd-tree (requires
generative recursion)

Draw a ray from a given point to infinity.  Decide if the ray
intersects the line segment $AB$.

Given a sequence of points that define a polygon, decide whether a
query point lies inside the polygon (requires at least lists; other
requirements unclear)