The ordered pair is nothing but a point on the coordinate graph. It is used to determine the position of a point in the cartesian plane. The more useful details regarding the ordered pair are provided below. Get an idea regarding the Ordered Pair Definition, Its Applications, and Solved Examples in the forthcoming modules.
Ordered Pair Definition
An ordered pair is the combination of coordinates which are x coordinate (abscissa) and y coordinate (ordinate). Those coordinates are real values enclosed by parenthesis and separated by a comma. The ordered pair is helpful to locate a point on the two-dimensional coordinate graph for better visual comprehension. The values in it can be integers or fractions.
Ordered Pair of a Coordinate System
Two numbers written in a certain order with parenthesis is also called an ordered pair. The usual representation of an ordered pair is (x, y). Where x is the horizontal value and y is the vertical value, and x, y are called the coordinates. The ordered pair (x, y) is never equal to the ordered pair (y, x). Whenever we write the coordinates of a point, first we write the x coordinate and then y coordinate value. As the ordered pair suggests the order in which values are written in a pair is very important.
Let us take a point P (2, 5)
The first number in the ordered pair shows the distance from the x-axis which is 2
The second number in the ordered pair shows the distance from the y-axis which is 5
To plot that point on the coordinate graph, count 2 steps towards the x-axis (towards the right) and start counting from the origin. And then 5 steps on the y-axis (upwards direction).
Applications:
- This concept is useful in data comprehension and statistics.
- The coordinate geometry uses ordered pairs to represent the geometric figures in an open space for virtual comprehension.
- Geometric shapes can be circles, triangles, squares, rectangle,s, and polygons use the ordered pairs to represent the center, vertices, and the length of the sides with coordinates.
Solved Example Questions
Example 1.
What are the coordinates of an ordered pair A (9, -7)?
Solution:
Given ordered pair is A (9, -7)
Its coordinates are x coordinate is 9 and the y coordinate is -7.
As the x coordinate is positive and the y coordinate is negative, the point belongs to the fourth quadrant.
Example 2.
Find out the abscissa and ordinates of a point P (-9, 7)?
Solution:
Given point is P (-9, 7)
The abscissa of the point is -9.
The ordinate of the point is 7.
As the point abscissa is a negative integer and ordinate is a positive integer the point lies in the third quadrant.
Example 3.
Is ordered pair A (5, 8) and B (8, 5) are equal?
Solution:
Given that,
A (5, 8) and B (8, 5)
The real numbers in both ordered pairs are the same. But both A and B are not equal.
Why because the first ordered pair A is having 5 as the x coordinate, 8 as the y coordinate, and the second ordered pair B (8, 5) is having 8 as the x coordinate and 5 as the y coordinate. So A ≠ B.
∴ Given ordered pairs, A and B are not equal.
FAQs on Ordered Pair of a Coordinate System
1. What is an example of an ordered pair?
Few examples of an ordered pair are (8, 6), (-8, 6), (8, -6), (-8, -6). All these ordered pairs are not equal. Because they belong to different quadrants.
2. What comes first in an ordered pair?
For every ordered pair, the x coordinate comes first followed by the y coordinate. It is important to write both coordinates in ordered pairs.
3. What is the order of an ordered pair?
An ordered pair is a pair of numbers present in a specific order and contains two numbers. The order in which you write those numbers is very important. Those numbers are called coordinates of a point. The x coordinate is the first number and y coordinate is the second number. The ordered pair is useful to locate a point in the coordinate plane.