/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 43 Do \((3,4)\) and \((4,3)\) corre... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 43

Do \((3,4)\) and \((4,3)\) correspond to the same point in the plane? Explain.

Short Answer

Expert verified
(3,4) and (4,3) are different points in the plane.

Step by step solution

01

Identify the Points

The points given are \( (3,4) \) and \( (4,3) \).
02

Understand Coordinate Notation

Points in the plane are denoted by \( (x, y) \), where \( x \) is the horizontal coordinate and \( y \) is the vertical coordinate.
03

Plot the Points on a Graph

Plot the point \( (3, 4) \) by moving 3 units along the x-axis and 4 units up the y-axis. Then, plot the point \[ (4, 3) \] by moving 4 units along the x-axis and 3 units up the y-axis.
04

Compare the Points

Note that \( (3, 4) \) and \( (4, 3) \) are in different locations because their x and y coordinates are swapped.
05

Draw the Conclusion

Since the points have different coordinates, they do not correspond to the same location in the plane.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

coordinates
Coordinates are pairs of numbers that indicate the position of a point on a coordinate plane. They follow the format \((x, y)\) where the first value \(x\) represents the horizontal position (how far left or right the point is), and the second value \(y\) represents the vertical position (how far up or down the point is). For instance, in the coordinate pair \((3, 4)\), the point is 3 units to the right of the origin along the x-axis and 4 units up along the y-axis.
coordinate plane
The coordinate plane is a two-dimensional surface on which we can locate points using coordinates. It is divided into four quadrants by the x-axis (horizontal line) and the y-axis (vertical line). The point where the x-axis and y-axis intersect is called the origin, denoted by \((0, 0)\). Every point on the plane is identified by a unique pair of coordinates that reflect its horizontal and vertical positions. Understanding the coordinate plane is crucial for graphing points and solving geometric problems.
graphing points
Graphing points is a method of representing coordinates on the coordinate plane. To graph a point \((x, y)\), you begin at the origin. Move horizontally to the position indicated by \(x\), and then move vertically to the position indicated by \(y\). This process helps visualize the location of points on the plane.

For example, to graph the points \((3, 4)\) and \((4, 3)\), start at the origin, move 3 units right and 4 units up for the first point, and 4 units right and 3 units up for the second point. By visualizing these movements, it's clear that \((3, 4)\) and \((4, 3)\) occupy different spaces on the coordinate plane even though they resemble each other numerically.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

What is the slope of a line whose graph is parallel to the graph of \(3 x+y=7 ?\) Perpendicular to the graph of \(3 x+y=7 ?\)

Write an equation for each line passing through the given point and having the given slope. Give the final answer in slope-intercept form. $$ (-3,1), m=-2 $$

Which equations are equivalent to \(2 x-3 y=6 ?\) $$ \begin{array}{ll}{\text { A. } y=\frac{2}{3} x-2} & {\text { B. }-2 x+3 y=-6} \\\ {\text { C. } y=-\frac{3}{2} x+3} & {\text { D. } y-2=\frac{2}{3}(x-6)}\end{array} $$

Concept Check Which of these equations have a graph with only one intercept? A. \(x+8=0\) B. \(x-y=3\) C. \(x+y=0\) D. \(y=4\)

Write the equation of each line with the given slope and \(y\) -intercept. $$ m=-1,(0,-7) $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.