Graphing a quadrilateral using a single Cartesian equation

Abstract

In this paper, we show that it is possible to graph an arbitrarily given quadrilateral (with known vertices) using only a single Cartesian equation. Crucially, we rely on matrix algebra; in particular, projective mappings which are commonly exploited in computer graphics but seldom mentioned in high school lessons or undergraduate matrix algebra courses. Our exploration is also helped by the use of a graphing calculator. Assuming no prior knowledge of matrices on the part of the reader, this paper introduces the necessary matrix-related machinery that our discussion requires.