In benidormclubdeportivo.orgematics, an notified pair is a set of two numbers commonly written in the kind (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 of an ordered pair
Ordered pairs are frequently used come specify a ar on a map or coordinate plane. Sometimes, a map will use a letter to represent among the numbers in the ordered pair.
In the above map of main America, coordinates are supplied to point out the location of a couple of countries: Mexico (B, 1), Belize (B, 3), Guatemala (C, 2), Honduras (C, 3), and also Nicaragua (D, 4). Top top the coordinate aircraft to the right, point out A and also B are specified utilizing the ordered pairs (3, -1) and also (2, -3), respectively.
Cartesian coordinate plane
The use of ordered bag is most often seen in the Cartesian coordinate plane. An bespeak pair, (x, y), is a collection of numbers the tells us the collaborates of a point in the coordinate plane. The very first number, dubbed the x-coordinate, synchronizes to a place on the x-axis, and also the 2nd number, referred to as the y-coordinate, coincides to a position on the y-axis.
Finding a point in the coordinate plane
To determine the position of a offered an bespeak pair, (x, y), start from the origin (0, 0), then counting x squares along the x-axis to determine the horizontal place of a point. To determine vertical position, count y squares along the y-axis, as displayed in the figure below.
Ordered pairs as solutions
The equipment to a two-variable equation or graph of one equation can also be written as an bespeak pair.
Below are three that the unlimited plenty of solutions to the equation y = -x + 3:
(-1, 4), (0, 3), and (2, 1).
We can verify this by trial and error whether or not:
1. The bespeak pair satisfies the equation (makes the equation a true statement once the coordinates of the notified pair space substituted into the equation).
Substituting the ordered pairs:
| 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 the the equation.
Since the three points space on the graph that y = -x + 3, presented above, the ordered pairs are options to the equation.
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Ordered pairs as vectors
In physics, a vector can be represented as an notified pair, , where the very first number is referred to as the vector"s x-component and the second number is called the vector"s y-component. The ordered pair suggests the position of a point on the coordinate plane through i beg your pardon a vector, beginning at the origin, passes.