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Topic Overview
Co-ordinate Geometry is a relatively modern branch of mathematics, but in its short history it has proved to be immensely useful. 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). One fundamental idea in co-ordinate geometry is that of the equation of a line. In this topic, we examine in detail the notion 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.
Question 2 on Paper 2 covers the co-ordinate geometry of the line, and is one of the most popular questions on the second paper. 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.
Topic Structure
The study of Senior Cycle Co-ordinate Geometry: The Line can be divided into the following sections:
Distance and Midpoint
Slope of a Line
Equation of a Line
Area of a Triangle
Links
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.
http://mathforum.org/dr.math/tocs/eq.gr.trans.high.html
Ask Dr Math consists of questions that have been put to 'Dr Math' and solutions to these questions from 'experts'. This particular link is to Equations, Graphs and Translations. Many questions are beyond our course, but some are relevant.
http://www.s-cool.co.uk/topic_quicklearn.asp?loc=ql&topic_id= 107&quicklearn_id=4&subject_id=1
This English site, s-cool, provides revision material for GCSE and A-levels. This link is to a part of the A-level section, but the material is relevant for our course. A fairly detailed explanation of many of the formulae and methods on our course is provided.
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