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Axes

All graphs have an \({x}\)-axis and a \({y}\)-axis.

Here is a diagram of a typical set of axes.

• The point \({(0,~0)}\) is called the origin.

• The horizontal axis is the \({x}\)-axis.

• The vertical axis is the \({y}\)-axis.

Key point

The x-axis is horizontal, and the y-axis is vertical.

One way to remember which axis is which is 'x is a cross so the \({x}\)-axis is across'.

Or you can remember’ y is up’ or ‘wise up’.

Coordinates

Coordinates are written as two numbers, separated by a comma and contained within round brackets.

For example, \({(2,~3)}\), \({(5,~7)}\) and \({(4,~4)}\).

• The first number refers to the \({x}\)-coordinate.

• The second number refers to the \({y}\)-coordinate.

Coordinates are written alphabetically - so x comes before y (x, y).

One way to remember is 'you go along the hallway before you go up the stairs'.

When describing coordinates, always count from the origin.

For example, to to describe the position of point A in the following diagram, start at the origin and move two squares in the horizontal (\({x}\)) direction.

Then move three squares in the vertical (\({y}\)) direction.

The coordinates of point A are therefore \({(2,~3)}\).

Similarly, the coordinates of point B are \({(8,~9)}\).

Remember the rule still applies for four quadrants: 'you always go along the hallway before you go up or down the stairs'.

Extending the \({x}\) and \({y}\) axes beyond the origin reveals the negative scales.

The regions separated by the axes are called quadrants.

There are four quadrants in total.

Coordinates in these quadrants are still described in terms of \({x}\) and \({y}\), but now the values of both \({x}\) and \({y}\) can be either positive or negative.

For example in the diagram opposite:

*The coordinates of A are \({(-2,~3)}\)*The coordinates of B are \({(-3,~-4)}\)