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An ordered pair is a pair formed by two elements that are separated by a comma and written inside the parantheses. For example, (x, y) represents an ordered pair, where 'x' is called the first element and 'y' is called the second element of the ordered pair.
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- What Is An Ordered Pair?
- Ordered Pair: Definition
- Ordered Pair in Cartesian Plane
- How to Graph Points Using Ordered Pairs
- Ordered Pairs in Different Quadrants
- Cartesian Product and Ordered Pairs
- Equality Property of Ordered Pairs
- Conclusion
- Solved Examples on Ordered Pairs
An ordered pair refers to two numbers written in a certain order.We generally use ordered pairs in the context of coordinates of a point in a 2D plane. It helps to locate or plot a point easily on a Cartesian plane. To represent an ordered pair, the two numbers are written inside the parentheses, separated by a comma, like this: (x, y) Here, “x” is...
An ordered pair is a pair of elements or numbers written in a specific and fixed order. On a Cartesian plane, an ordered pair (x, y) is defined as the coordinatesof a point such that “x” is the x-coordinate and “y” is the y-coordinate. Ordered pair examples: (1,2), (-4, 5), (-9, -8)
The Cartesian plane is named after a French mathematician, René Descartes, who first introduced it. It is formed by the intersection of two perpendicular number lines (or axes). We call the horizontal axis the x-axis and the vertical axis the y-axis. The two axes intersect at the origin. An ordered pair represents the position of a point on the coo...
Step 1:Start with the first number “x” in the ordered pair or the x-coordinate. 1. If x is positive, move |x| units to the right of the origin. 2. If x is negative, move |x| units to the left of the origin. Mark this point. Step 2:Next, we will consider the second number in the ordered pair or the y-coordinate. We will move vertically up or down fr...
The x-axis (horizontal axis) and the y-axis (vertical axis) divide the Cartesian plane into 4 parts. Each of the 4 parts is known as a quadrant. The signs of x and y in an ordered pair (x, y) in a particular quadrant can be determined on the basis of the two number lines that form axes of the given quadrant. Similarly, you can easily identify in wh...
The cartesian product A B of two non-empty sets A and B is basically the collection of all ordered pairs (a, b) such that the first element “a” is from the set A and the second element “b” is from the set B. A×B={(a,b):a∈A,b∈B} Example: A={1,2},B={5,6} A×B={(1,5),(1,6),(2,5),(2,6)}
If two ordered pairs are equal, then their corresponding elements are also equal. This is known as the “equality property of ordered pairs.” If (x, y) = (a, b) then we can say that x = a and y = b. 1. If (x, y) = (1, 5) then x = 1 and y = 5. 2. If (a, b)= (c, d), then a = c and b = d. 3. If (x + 1, y +1) = (10, 12) then x + 1 = 10 and y + 1 = 12.
In this article, we learned about ordered pairs, their representation, ordered pairs on a Cartesian plane, ordered pairs in a Cartesian product, and equality property. Let’s look at a few solved examples and practice problems.
1. What does the ordered pair (5, –6) represent on the Cartesian plane? Solution: The first element of (5, -6) = x-coordinate = 5 It is positive. It means that the horizontal distance of the point from origin is 5 units to the right. The second element of (5, -6) = y-coordinate = -6 It is negative. It means that the vertical distance from origin is...
May 31, 2024 · What is an Ordered Pair? An ordered pair is a fundamental concept in mathematics, representing a pair of elements arranged in a specific order. In mathematical notation, an ordered pair is typically written as (x, y) where ‘x’ and ‘y’ are the elements of the pair.
In mathematics, an ordered pair, denoted (a, b), is a pair of objects in which their order is significant. The ordered pair (a, b) is different from the ordered pair (b, a), unless a = b. In contrast, the unordered pair, denoted {a, b}, equals the unordered pair {b, a}.
In an ordered pair, (x, y), the first element ‘x’ is called the abscissa and the second element ‘y’ is called the ordinate. Let us look at a couple of examples of how ordered pairs are represented on the coordinate plane.
Nov 21, 2023 · Definition & Example. An ordered pair such as (3,-1), is a shorthand way of writing two variables, such as x = 3 and y = -1. The order of the numbers in the pair is important: x always comes...
An ordered pair is a set of two numbers or objects in which the order of the elements matters. It is often written in parentheses (like this: (4,5)). The first number is the x-coordinate, and the second is the y-coordinate.
