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Chapter 3: Problem 1

Fill in the blanks. \((7,1)\) is called an __pair.

Short Answer

Expert verified
Ordered pair.

Step by step solution

01

Identify the concept

Recognize that the term 'pair' is associated with order and sequence. In mathematics, particularly in coordinate geometry, a pair of numbers such as \(7,1\) is often referred to using a specific term.
02

Recall the term

The specific term used to describe a pair of numbers in a sequence like \(x,y\) is called an 'ordered pair'. This distinguishes it from other non-sequential pairings of numbers.
03

Fill in the blank

Since the pair given is \(7,1\), it is called an ordered pair. Therefore, the answer to the blank is 'ordered.'

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Key Concepts

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

Coordinate Geometry
Coordinate geometry, also known as analytic geometry, provides a link between algebra and geometry through graphs. It allows us to describe geometric figures using numbers and equations. The fundamental concept involves the coordinates of points on a plane, often represented as ordered pairs. For example, the point
  • \((7, 1)\) signifies a location 7 units along the x-axis (horizontal) and 1 unit up the y-axis (vertical).
By using coordinate geometry, we can:
  • Determine distances between points.
  • Find the midpoint of a line segment.
  • Calculate slopes of lines.
This branch of mathematics is indispensable for solving problems related to shapes, lines, and curves on a plane.
Ordered Pair Definition
An ordered pair consists of two elements arranged in a specific order, denoted by the notation \((x, y)\). This is crucial in coordinate systems. The first number represents the horizontal position (x-coordinate), and the second number represents the vertical position (y-coordinate). For example:
  • In the pair \((7, 1)\), 7 is the x-coordinate, and 1 is the y-coordinate.
The order of these numbers matters. Switching them changes their position on the graph. This importance of order underscores the definition of 'ordered pair,' as opposed to just any pair of numbers. Ordered pairs are foundational in many areas of math, including functions and relations.
Mathematical Sequences
Mathematical sequences are lists of numbers arranged in a particular order. Each number in the sequence is called a term. Sequences can be finite or infinite and may follow specific rules or patterns. Some examples include:
  • Arithmetic sequences, where each term is a constant amount larger than the previous one (e.g., 2, 4, 6, 8).
  • Geometric sequences, where each term is a constant ratio of the previous one (e.g., 3, 6, 12, 24).
In the context of coordinate geometry, sequences can describe the path of movement along a line or curve by listing the points visited in order. Understanding sequences helps in predicting future terms and creating mathematical models for various applications.

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Most popular questions from this chapter

Parts Lists. The function \(f(r)=2.30+3.25(r+0.40)\) approximates the length (in feet) of the belt that joins the two pulleys, where \(r\) is the radius (in feet) of the smaller pulley. Find the belt length needed for each pulley in the parts list. CAN'T COPY THE IMAGE $$ \begin{array}{|c|c|} \hline & {\text { Parts list }} \\ \hline \text { Pulley } & {r} & {\text { Belt length }} \\ \hline P-45 M & {0.32} \\ {P-08 D} & {0.24} \\ \hline \end{array} $$

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