In jajalger2018.orgematics, an ordered pair is a set of 2 numbers generally written in the type (a, b). The bespeak of the two numbers is important—(a, b) is various from (b, a) unless a equals b.

You are watching: The second number in an ordered pair

Ordered bag are frequently used come specify a place on a map or name: coordinates plane. Sometimes, a map will use a letter come represent among the numbers in the ordered pair.

In the above map of main America, coordinates are supplied to specify the positions of a few countries: Mexico (B, 1), Belize (B, 3), Guatemala (C, 2), Honduras (C, 3), and also Nicaragua (D, 4). ~ above the coordinate aircraft to the right, point out A and also B space specified utilizing the ordered bag (3, -1) and also (2, -3), respectively.

## Cartesian name: coordinates plane

The use of ordered pairs is most regularly seen in the Cartesian coordinate plane. An ordered pair, (x, y), is a set of numbers that tells us the works with of a allude in the name: coordinates plane. The first number, dubbed the x-coordinate, synchronizes to a position on the x-axis, and also the second number, dubbed the y-coordinate, corresponds to a place on the y-axis.

### Finding a allude in the coordinate plane

To determine the place of a given an ordered pair, (x, y), start from the origin (0, 0), then count x squares along the x-axis to identify the horizontal place of a point. To identify vertical position, count y squares follow me the y-axis, as displayed in the number below.

### Ordered pairs together solutions

The systems to a two-variable equation or graph of an equation can additionally be composed as an ordered pair.

Below space three of the unlimited many solutions to the equation y = -x + 3:

(-1, 4), (0, 3), and (2, 1).

We deserve to verify this by experimentation whether or not:

1. The bespeak pair satisfies the equation (makes the equation a true statement once the coordinates of the notified pair are substituted into the equation).

Substituting the notified pairs:

(-1, 4)(0, 3)2, 1)4 = -(-1) + 34 = 1 + 34 = 4 | 3 = -(0) + 33 = 3 | 1 = -(2) + 31 = -2 + 31 = 1 |

2. The ordered pairs room points top top the graph that the equation.

Since the three points are on the graph that y = -x + 3, displayed above, the ordered bag are services to the equation.

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### Ordered pairs together vectors

In physics, a vector can be represented as an notified pair, , whereby the very first number is dubbed the vector"s x-component and the 2nd number is called the vector"s y-component. The ordered pair suggests the position of a allude on the coordinate aircraft through i beg your pardon a vector, beginning at the origin, passes.