In **analytic geometry**, we study geometry using algebra. The first step is to find a way to translates points into numbers, called *coordinates.*

## The number line

You are probably familiar with the idea of the *number line*. Each point of the number line corresponds to a unique number. Remember that in geometry, lines are in principle infinitely long; no matter how big or small a number is, it will fit on the number line.

The number belonging to each point is called the **coordinate** of that point. Conversely, if *x* is a number then (*x*) stands for the corresponding point on the number line. For instance, (0) represents the “zero point”, or **origin** of the number line.

Using these coordinates, we can translate the *geometry* of the points on the line into facts of *algebra*. The table below shows some basic examples.

geometry | algebra |
---|---|

(x) lies to the left of the origin | x < 0 |

(x) lies to the left of (y) | x < y |

the distance between (x) and (y)= the length of the line segment with endpoints ( x) and (y) | |x – y| |

the line segment with endpoints (x) and (y) is longer than the line segment with endpoints (a) and (b) | $ latex |x – y| < |a – b| |

Translate into an algebra statement: (*x*) lies between points (*a*) and (*b*).

If (*p*) and (*q*) are points, which point (*m*) is described by the equation *m* = (*p* + *q*)/2 ?