# 3 Coordinates and graphs

## 3.1 Positive coordinates

For many towns and cities, an individual book of street maps called an A to Z has been produced. You can look up the name of a street in the index, and it will give you the page number of the map that contains the street, plus the *grid reference* square for the street. There are different conventions for these grid references. You may have met several of these.

### Example 8

The index in an A to Z gives the reference for School Lane as:

To find School Lane on the map, turn to page 17 in the A to Z, move across to column F and then go to row 4:

Similarly, the grid reference for Rickland Place on page 17 in the A to Z is E2.

In mathematics, locating points on a grid is similar to finding a place on a map by means of grid references. However, the grid lines themselves are labelled, rather than the squares. For example, on the grid below, the point A is located by moving across 3 and then up 2.

In the same way that the grid references on a map are based on a starting point – in Example 8 the starting point was the bottom left corner of the map (column A, row 1) – a starting point is needed to locate points on a mathematical grid. This starting point is called the **origin**. From the origin you can move horizontally across and vertically up: the line across is called the **horizontal axis**, and the line going up is called the **vertical axis**.

On a mathematical grid, the horizontal axis is often labelled the ** x-axis**, and the vertical axis is labelled the

**. Scales are indicated on the axes to aid the location of points, and the origin is usually labelled 0.**

*y*-axisThe distance *across* to a point is called the ** x-coordinate** of the point, and the distance

*up*to a point is called the

**of the point. So, in the example below, A is located at the point with**

*y*-coordinate*x*-coordinate 3 and

*y*-coordinate 2.

The coordinates of a point are written in brackets, with the *x*-coordinate followed by the *y*-coordinate, separated by a comma. Thus the coordinates of the point *A* above are written:

### Example 9

Write down the coordinates of the points *A* and *B*.

#### Answer

To locate *A*:

start at the origin;

move

*across*1 unit;move

*up*3 units.

The coordinates of *A* are (1, 3).

To locate *B*:

start at the origin;

move

*across*2 units;move

*up*0 units.

The coordinates of *B* are (2, 0).