Define an ordered pair.

An ordered pair is a set of two elements arranged in a specific sequence, usually written as (x, y).

In mathematics, an ordered pair is used to represent a point in a coordinate system, such as the Cartesian plane. The first element of the pair, often denoted as 'x', represents the horizontal position, while the second element, 'y', represents the vertical position. For example, the ordered pair (3, 5) indicates a point that is 3 units to the right of the origin and 5 units up.

The order of the elements in the pair is crucial because (x, y) is not the same as (y, x). For instance, (2, 4) and (4, 2) represent different points on the Cartesian plane. This specific sequence allows us to accurately locate and distinguish points in a two-dimensional space.

Ordered pairs are also used in various mathematical contexts beyond geometry, such as in functions and relations. In a function, each input (x) is paired with exactly one output (y), and this relationship can be represented using ordered pairs. For example, if we have a function f(x) = x + 2, the ordered pair (3, 5) shows that when x is 3, the output y is 5.

Understanding ordered pairs is fundamental in GCSE Maths as it forms the basis for graphing equations, analysing functions, and solving coordinate geometry problems.