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An ordered pair (x, y) is used to represent the location of a point in coordinate geometry where x is the horizontal distance and y is the vertical distance of the point. An ordered pair (x, y) represents an element of a relation R which is denoted by xRy (x "is related to" y). If (x, y) = (a, b) then x = a and y = b.
- 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...
Ordered Pair. more ... Two numbers written in a certain order. Which can be used to show the position on a graph, where the "x" (horizontal) value is first, and the "y" (vertical) value is second. So (12,5) is 12 units along, and 5 units up. Illustrated definition of Ordered Pair: Two numbers written in a certain order.
Video transcript. Below are ordered pairs that represent the first six terms of two given patterns. The first value in each pair is a term from pattern A. And the second value is a term from pattern B. In the answer box, there are different statements about the two patterns. Choose all correct statements.
- 5 min
- Sal Khan
An ordered pair is a pair of mathematical objects in which the order of the objects is significant. It is commonly used to represent the coordinates of a point in a two-dimensional plane. It is commonly used to represent the coordinates of a point in a two-dimensional plane.
Ordered pair. Analytic geometry associates to each point in the Euclidean plane an ordered pair. The red ellipse is associated with the set of all pairs ( x, y) such that x2 4 + y2 = 1. In mathematics, an ordered pair ( a, b) is a pair of objects. The order in which the objects appear in the pair is significant: the ordered pair ( a, b) is ...
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Ordered pairs. In mathematics, an ordered pair is a set of two numbers usually written in the form (a, b). The order of the two numbers is important— (a, b) is different from (b, a) unless a equals b. Ordered pairs are commonly used to specify a location on a map or coordinate plane. Sometimes, a map will use a letter to represent one of the ...
