Co-ordinate geometry

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Co-ordinate geometry

A place for everything, and everything in its place

Samuel Smiles

Co-ordinates

Co-ordinates are a means of describing a position relative to some fixed point,

or origin. In two dimensions you need two pieces of information; in three

dimensions, you need three pieces of information.

In the Cartesian system (named after René Descartes), position is given in

perpendicular directions: x, y in two dimensions; x, y, z in three dimensions (see

figure 2.1). This chapter concentrates exclusively on two dimensions.

Ahead for 3 blocks,

turn right, then continue

for 5 blocks.

Fly for 3 km on a

bearing of 360°.

Travel on bus

turn right, then continueAhead for 3 blocks, 34 for 8 stops.

for 5 blocks.

Travel on bus

34 for 8 stops.

0 1

–1

–1 2 3 4

1

2

3

y

x

2

3 (3, 2)

y

x

0 1

–1

–1 2 3 4

1

2

3

y

x

2

3 (3, 2)

5

0 1

–1

2 3

3

4

4

–1 –1

–2

–3

–4

2 1

3

–2

1

2

3

4

z

y

x

5

(3, 4, 5)

4

5

Figure 2.1

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