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In math, an ordered pair is a pair of two elements (numbers or variables or combination of both number and variable) that is of the form (x, y) where the order of the elements x and y is important. It means (x, y) may/may not be equal to (y, x).
May 31, 2024 · In mathematical notation, an ordered pair is typically written as (x, y) where 'x' and 'y' are the elements of the pair. An ordered pair denoted as (x, y), maintains the sequence of its elements while an unordered pair does not consider the order. For example, (1, 2) is distinct from (2, 1) in ordered pairs but they represent the same set in ...
Nov 20, 2020 · Solution: As per the equality of ordered pairs, the two ordered pairs will be equal only if the corresponding first components and second components are equal. As per the above statement, we can write the equation as. 2x-2 = x+3 , y-1 = 4. Solve the expressions and find the values of x, y easily. 2x-x = 3+2.
- 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...
Sep 17, 2024 · Both the elements of an ordered pair can be the same but they are not equal. Ordered Pairs Examples. Example 1: Calculate the values of a and b if two ordered pairs (a, b) and (7, 8) are equal. Solution: Given two ordered pairs are (a, b) and (7, 8) Two ordered pairs are equal means their corresponding elements are also equal.
Jan 14, 2024 · A relation from set A to set B is a set of ordered pairs where the first element is from set A and the second element is from set B. If every element in set A is paired with exactly one element in set B, we have a function. For example, if we have two sets A = {1, 2, 3} and B = {4, 5, 6}, an example of a relation from A to B could be the set of ...
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Jul 30, 2024 · Two ordered pairs are equal if and only if corresponding coordinates are equal: $\tuple {a, b} = \tuple {c, d} \iff a = c \land b = d$ Proof Necessary Condition.
