Examples on Ordered Pair
Example 1: Plot the point (2, -3) on a Cartesian coordinate plane.
Solution:
Start at the origin (0, 0)
Move 2 units to the right (positive x-direction)
Move 3 units downward (negative y-direction)
Plot the point at (2, -3)
Example 2: Determine which quadrant the point (-4, 5) lies in.
Solution:
Since x-coordinate is negative and the y-coordinate is positive, the point lies in the second quadrant.
Example 3: Find the Cartesian product of the sets {1, 2} and {a, b}.
Solution:
Cartesian product is {(1, a), (1, b), (2, a), (2, b)}.
Example 4: Verify if the ordered pairs (3, 4) and (4, 3) are equal.
Solution:
Since first elements are different (3 ≠ 4), and the second elements are also different (4 ≠ 3), the ordered pairs are not equal.
Example 5: Determine the midpoint of the line segment with endpoints (1, 3) and (5, -1).
Solution:
Midpoint formula: ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Midpoint = ((1 + 5) / 2, (3 + (-1)) / 2)
= (6 / 2, 2 / 2)
= (3, 1)
Example 6: If (a, b) = (3, -2), what are the values of ‘a’ and ‘b’?
Solution:
‘a’ is First element of the ordered pair, so a = 3
‘b’ is Second element of the ordered pair, so b = -2
Ordered Pair
In mathematics, an ordered pair is a fundamental concept used to represent the coordinates of a point in a coordinate plane. It consists of two values, typically denoted as (x, y), where the first value represents the horizontal position (abscissa) and the second value represents the vertical position (ordinate).
In this article, we will learn about, Ordered Pair definition, Potting order pair, examples of ordered pairs and others in detail.
Table of Content
- What is an Ordered Pair?
- Ordered Pair Definition
- Ordered Pair in Coordinate Geometry
- Ordered Pairs in Different Quadrants
- Graphing Ordered Pairs
- Ordered Pair in Sets
- Properties of Ordered Pairs
- Equality Property of Ordered Pairs
- Cartesian Product and Ordered Pairs
- Facts about Ordered Pairs
- FAQs on Ordered Pair