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 also 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.

For this course the study of the Line can be divided into the following sections:

Distance and Midpoint

If you draw this out on a graph so that a right angle triangle is formed by the line segment and lines parallel to the X and Y axis through the points at each end of the line segment you can see that this is actually an application of Pythagoras’ theorem.

Slope of a Line

If lines are parallel, their slopes are the same.

Equation of a Line

Area of a Triangle

http://www.math.armstrong.edu/MathTutorial/index.html
This site includes some material relevant to coordinate geometry. Each link brings you through to a number of questions on that topic, and by clicking on the question number, you are shown a worked solution of that question.