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Chapter 5: Problem 55

Why is the point \((x, y)\) called an ordered pair?

Short Answer

Expert verified
The point (x, y) is called an ordered pair because the order of the coordinates uniquely identifies a specific location in a coordinate system.

Step by step solution

01

Understanding the Components

Consider the point (x, y). It consists of two numbers, x and y. The first number in this pair is called the x-coordinate, and the second number is called the y-coordinate.
02

Order Matters

In an ordered pair, the sequence in which the coordinates are listed is crucial. The x-coordinate always comes first, and the y-coordinate comes second. This order must be maintained to accurately represent a specific point in a coordinate system.
03

Unique Representation

The specific order of the coordinates ensures that each ordered pair uniquely identifies a point on a graph. Changing the order will lead to a different location. For example, (2, 3) is different from (3, 2).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ordered Pairs
An ordered pair, such as (x, y), is a fundamental concept in mathematics. It's called an 'ordered pair' because the order in which the numbers appear is important.
The first number in the pair is known as the x-coordinate, and the second is the y-coordinate.
This structure allows us to exactly pinpoint a location on a graph.

It's significant to remember that (x, y) is different from (y, x).
For instance, (2, 3) will be a different point on the graph from (3, 2).
Thus, the name 'ordered pair' emphasizes the necessity of sequence.
Changing the sequence of x and y will locate a different point in the coordinate system.
x-coordinate
The x-coordinate is the first number in an ordered pair (x, y).
It shows the horizontal position of the point on a graph.

To locate the x-coordinate, you start from the origin point (0,0) and move horizontally:
  • Move right if the x-coordinate is positive.
  • Move left if the x-coordinate is negative.
For example, in the pair (3, 2), the x-coordinate is 3.
This means you move 3 units to the right from the origin.

Getting comfortable with x-coordinates helps in better understanding and plotting points on a graph efficiently.
y-coordinate
The y-coordinate is the second number in an ordered pair (x, y).
It indicates the vertical position of the point on a graph.

To find the y-coordinate, after determining the x-coordinate, you move vertically:
  • Move up if the y-coordinate is positive.
  • Move down if the y-coordinate is negative.
For instance, in the pair (3, 2), the y-coordinate is 2.
This shows you need to move 2 units up from the x-position.

By understanding how to locate y-coordinates, you can accurately plot the vertical aspects of points on a coordinate system.

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