ABSTRACT
We have collected a number of definitions and results in elementary Plane Geometry, and listed some trigonometric formulae. The reader should ab sorb these carefully.
0.1 Cartesian coordinates
Points in the plane can be represented by coordinates (x,y). We choose as origin a fixed point O in the plane. The positive x-axis is a half-line* Ox beginning at the origin, and the positive y-axis Oy is the half-line also beginning at the origin obtained by rotating Ox counter-clockwise through an angle —. Rarely we may consider the ?/-axis Oy to be obtained by
rotating the first clockwise through an angle —. The x-axis is the whole
line containing Ox and the ?/-axis is the whole line containing Oy. Any point P in the plane can be written uniquely in the form (x,y) where x is
the directed length (it can be negative) in the direction Ox of the projection of OP onto the x-axis, and y is the directed length in the direction Oy of the projection of OP onto the y-axis (see Figure 0.1). These lengths are measured in the appropriate units or scaled units. The position vector of P is r = {x,y). The set of ordered pairs (x,y) of real numbers is denoted by R2 . A choice of origin and (directed) axes gives an identification of the plane with R2 . Where appropriate we write 'the plane R2 '.
