Axes, origin and points on the axes

The number line you know is one-dimensional: it only goes left and right. To mark points on a flat surface (2-D), we use two number lines at right angles.

• The flat one is the x-axis.
• The upright one is the y-axis.
• They meet at the origin, O, whose coordinates are (0, 0). ('Axes' is the plural of 'axis'.)

Both axes have equal units. Right of O and up from O are positive. Left of O and down from O are negative.

Points on the axes (Fig. 1.2):

• B is on the x-axis, 4.5 units right of O, so B = (4.5, 0).
• G is on the y-axis, 4.5 units below O, so G = (0, –4.5).
• H is on the y-axis, 4 units above O, so H = (0, 4).

The pattern: on the x-axis the y-coordinate is always 0, so the point is (x, 0). On the y-axis the x-coordinate is always 0: (0, y). The other number tells you how far, and its sign tells you which way.

We often drop the '=' and write P (x, y) instead of P = (x, y).

Reiaan's room on the axes (Fig. 1.3): O (0, 0) is one corner. His door runs from D1 (8, 0) to R1 (11.5, 0), and the bathroom door from B1 (0, 1.5) to B2 (0, 4).