Co-ordinate Geometry of the Line

Co-ordinate Geometry is a relatively modern and immensely useful branch of mathematics. The idea of giving points in the plane co-ordinates makes it much easier to deal with many properties of geometry that had previously been tackled using so-called Euclidean geometry (i.e., theorems).

Coordinates are pairs of numbers that are used to determine points in a plane, relative to a special point called the origin. The origin has coordinates (0, 0).

One fundamental idea in co-ordinate geometry is that of the equation of a line. In this topic, we examine the idea of the equation of a line and its properties, e.g., slope. We also consider other basic concepts such as distance, midpoint and the area of a triangle.

It is important to note that many of the ideas from this topic come into many others, e.g., the circle, graphs and linear programming. There is also a very close link between the Argand diagram in Complex Numbers and co-ordinate geometry.