Calculations for purposes of partitioning land—that is, cutting off a portion of a
tract for title transfer—can be aided significantly by using coordinates. For example,
suppose the owner of the tract of land in Figure 12.5 wishes to subdivide the
parcel with a line GF, parallel to AE, and have 3.000 acres in parcel AEFG. This
problem can be approached by three different methods. The first involves trial
and error, and works quite well given today’s computing capabilities. The second
consists of writing equations for simple geometric figures such as triangles, rectangles,
and trapezoids that enable a unique solution to be obtained for the coordinates
of points F and G. The third approach involves setting up a series of
coordinate geometry equations, together with an area equation, and then solving
for the coordinates of F and G. The following subsections describe each of the
above procedures.