/*! 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 24 Graph and label each point on a ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 24

Graph and label each point on a coordinate plane. Name the quadrant in which each point is located. $$B(-5,-5)$$

Short Answer

Expert verified
Point B(-5,-5) is in the third quadrant.

Step by step solution

01

Identify the Coordinates

The coordinates given are \( B(-5, -5) \), which means the point is located at \( -5 \) on the x-axis and \( -5 \) on the y-axis.
02

Plot the Point

To plot the point \( B(-5, -5) \) on a coordinate plane, start at the origin \((0,0)\) and move 5 units to the left along the x-axis because the x-coordinate is \(-5\). Then, move 5 units down along the y-axis, since the y-coordinate is \(-5\). Mark this point as \( B \).
03

Determine the Quadrant

The quadrant in which a point is located depends on the signs of its x and y coordinates. For \( B(-5, -5) \), both coordinates are negative. This placement is characteristic of the third quadrant of the coordinate plane, which is where both x and y are negative.

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.

Plotting Points
Plotting points on a coordinate plane is the process of placing a point at specific coordinates defined by an x-value and a y-value. The coordinate plane is divided into four quadrants and centered around the origin.
The origin is the point where the x-axis and y-axis intersect, denoted as (0, 0). This serves as the starting point for plotting any point.
  • To plot a point like B(-5, -5), you start at the origin (0, 0).
  • Move left or right along the x-axis according to the x-coordinate value. In our example, move 5 units left to -5, as the x-value is negative.
  • Then, move up or down the y-axis according to the y-coordinate value. Again, for B(-5, -5), move 5 units down because the y-value is also negative.
The coordinates (x, y) always define how you travel from the origin, making it easy to identify the precise location of any point on the plane.
Quadrants
A coordinate plane is divided into four different areas called quadrants. Each quadrant represents a specific combination of positive and negative x and y coordinates. This division helps in identifying where a point is located based on its coordinates.
  • The first quadrant is in the top right and has both x and y coordinates positive (e.g., (5, 5)).
  • The second quadrant is in the top left with a negative x and a positive y coordinate (e.g., (-5, 5)).
  • The third quadrant is in the bottom left where both coordinates are negative (e.g., (-5, -5)).
  • The fourth quadrant is in the bottom right and has a positive x coordinate and a negative y coordinate (e.g., (5, -5)).
Knowing which quadrant a point like B(-5, -5) is in (the third quadrant) quickly tells you the sign of the x and y coordinates.
X-axis and Y-axis
The x-axis and y-axis are two number lines that intersect at the origin (0, 0). Together, they lay the foundation for the coordinate plane, splitting it into four distinct sections or quadrants.
  • The x-axis is horizontal and represents the value of x in coordinates. Moving right from the origin increases x values positively, while moving left decreases them negatively.
  • The y-axis is vertical and signifies the y value in coordinates. Moving up from the origin makes y values positive, whereas moving down results in negative y values.
These axes form a grid upon which any point can be plotted. For example, in B(-5, -5), the x-value of -5 tells us to move left from the origin along the x-axis, and the y-value of -5 instructs a downward move along the y-axis.
Negative Coordinates
Negative coordinates indicate direction on both the x-axis and y-axis. When an x or y coordinate has a negative sign, it guides you to move left on the x-axis or down on the y-axis.
  • For an x-coordinate like -5, rather than moving right on the x-axis, move 5 units left.
  • For a y-coordinate like -5, move 5 units down instead of up.
Negative coordinates are always pivotal in locating points in the third and second quadrants of the coordinate plane. For instance, when plotting B(-5, -5), you navigate using both left and downward movements due to the negative signs, placing the point firmly within the third quadrant.

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

Find each sum or difference. $$36-19$$

Evaluate each expression if \(a=0, b=3,\) and \(c=-4\) $$|c|-a$$

OPEN ENDED Write two inequalities using integers

Find each quotient. $$40 \div 8$$

Evaluate each expression if \(a=0, b=3,\) and \(c=-4\) $$a+b+|c|$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Decision Maths

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.