7 Coordinate Geometry
Coordinate Geometry turns ‘diagrammatic’ geometry of the sort discussed in Chapter 5
into algebraic and numerical equations. It is the language that we have to use when ‘talking’
to computers about geometry. Here we focus on the essential basics that are needed in
science and engineering mathematics.
Prerequisites
It will be helpful if you know something about:- plotting graphs and simple plane coordinate systems (91
➤
) - Pythagoras’ theorem (154
➤
) - ratio and proportion (14
➤
) - systems of linear equations (48
➤
) - intercept theorem (153
➤
) - simple trig ratios and identities (175
➤
)- completing the square (66
➤
)Objectives
In this chapter you will find:- coordinate systems in a plane
- distance between two points in Cartesian coordinates
- midpoint and gradient of a line segment
- equation of a straight line
- parallel and perpendicular lines
- intersection of lines
- equation of a circle
- parametric representation of curves
Motivation
You may need the material in this chapter for:- geometrical aspects of calculus (➤Chapter 10)
- numerical methods
- study of laws converted to straight line form (135
➤
)- linear regression in statistics
- vectors (➤Chapter 11)