Definition
Ordered pair
An ordered pair is two values written in a fixed order, often to locate a point as (x, y).
What it means
An ordered pair gives two instructions in order. On a coordinate grid, start at the origin: the first number tells how far to move along the x-axis, and the second tells how far to move along the y-axis.
Remember it
Across first, then up or down: x before y.
Example
To plot (3, 5), move 3 units along the x-axis and then 5 units along the y-axis. The point (5, 3) is different because the two instructions have swapped places.
Watch for
The unordered collection {3, 5} does not choose a first and second value, so it is not the same as the ordered pair (3, 5).
Common mix-up
Do not read (x, y) as “up, then across.” The x-coordinate comes first.
Exact meaning
An ordered pair is a pair of values whose positions matter. On a Cartesian coordinate plane, (x, y) gives the horizontal coordinate first and the vertical coordinate second; reversing the values generally names a different point.