You write an ordered pair as two numbers enclosed in parentheses and separated by a comma, like (x, y).
Understanding Ordered Pairs
An ordered pair is a fundamental concept in mathematics used primarily to locate a point on a coordinate plane. It consists of two values written in a specific order, hence the name "ordered pair."
Components of an Ordered Pair
An ordered pair is always written in the format:
(x-coordinate, y-coordinate)
- x-coordinate: This is the first number in the pair. It represents the horizontal position of the point on the coordinate plane.
- y-coordinate: This is the second number in the pair. It represents the vertical position of the point on the coordinate plane. As noted in the reference, the number on the vertical axis is often called Y.
Standard Format
The standard way to write an ordered pair involves:
- Starting with an opening parenthesis
(. - Writing the x-coordinate.
- Adding a comma
,. - Writing the y-coordinate.
- Closing with a parenthesis
).
For example, an ordered pair representing a point where the horizontal position is 3 and the vertical position is 5 is written as (3, 5).
Based on the reference provided, when identifying a point, you determine the value on the horizontal axis (the x-coordinate) and the value on the vertical axis (the y-coordinate). For instance, if the vertical axis number (Y) is 9, this number will be the second value in your pair. You then enclose these two values within parentheses (or "brackets" as they are sometimes informally called) to form the ordered pair.
Example
Let's say you need to write the ordered pair for a point that is located at 4 on the horizontal axis and 7 on the vertical axis.
- The x-coordinate is 4.
- The y-coordinate is 7.
Following the standard format, the ordered pair is written as (4, 7).
If we take the example structure implied by the reference, where a point might be described as having an x-value of "one" and a y-value of "nine" (derived from the vertical axis measurement), you would write it as (1, 9). Once you have these two numbers, you "close my brackets" to complete the pair.
X vs. Y in Ordered Pairs
It's crucial to remember the order: the x-coordinate always comes first, followed by the y-coordinate.
| Coordinate | Position in Pair | Represents | Axis on Graph |
|---|---|---|---|
| x-coordinate | First (left) | Horizontal position | Horizontal (X) |
| y-coordinate | Second (right) | Vertical position | Vertical (Y) |
By consistently using the (x, y) format within parentheses, you can accurately represent any point in a two-dimensional coordinate system.
