
Coordinate geometry is one of the most useful bridges between the realms of diagrams and numbers. As we shall see, it is a two-way bridge; we can solve geometry problems in terms of numbers and also infer certain facts about numerical problems from figures.
1. Cartesian coordinates
(a) Lines and circles
(b) The slope-intersection form
(c) The section formula
(d) The distance formula
(e) Area of a triangle
(f) Graphs of real-valued functions
2. Polar coordinates
(a) Construction of the bijection
(b) Sketching curves