/*! 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 22 Plot each group of points. $$ ... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 22

Plot each group of points. $$ (-2,-4),(4,-3),(5,4),(-1,0),(-4,4),(0,5) $$

Short Answer

Expert verified
The points have been plotted on the Cartesian plane using their given coordinates.

Step by step solution

01

- Understand the Problem

The aim is to plot the given points on a Cartesian plane. Each point is given in the form \((x,y)\) where \(x\) is the x-coordinate and \(y\) is the y-coordinate.
02

- Identify the Coordinates

List out the coordinates of each point: 1. Point A: \((-2,-4)\) 2. Point B: \((4,-3)\) 3. Point C: \((5,4)\) 4. Point D: \((-1,0)\) 5. Point E: \((-4,4)\) 6. Point F: \((0,5)\)
03

- Draw the Axes

Draw the x-axis (horizontal) and y-axis (vertical) intersecting at the origin \((0,0)\). Make sure to label the positive and negative directions on both axes.
04

- Plot Each Point

Locate and mark each point on the Cartesian plane: 1. Mark Point A at \((-2,-4)\): 2 units left and 4 units down from the origin. 2. Mark Point B at \((4,-3)\): 4 units right and 3 units down. 3. Mark Point C at \((5,4)\): 5 units right and 4 units up. 4. Mark Point D at \((-1,0)\): 1 unit left on the x-axis. 5. Mark Point E at \((-4,4)\): 4 units left and 4 units up. 6. Mark Point F at \((0,5)\): 5 units up on the y-axis.
05

- Final Checking

Review the positions of all marked points to ensure they are correctly placed according to their coordinates.

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Key Concepts

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

Coordinates
Coordinates are a pair of numbers \(x,y\) that represent a specific point on a Cartesian plane. The first number is the x-coordinate, which tells us how far left or right to go from the origin \(0,0\). The second number is the y-coordinate, which tells us how far up or down to move.
For example, in the point \(-2,-4\), \(-2\) is the x-coordinate and \(-4\) is the y-coordinate. Together, coordinates let us locate exact positions in a two-dimensional space.
Coordinates are crucial for various applications such as graphing equations, mapping locations, and even in video games for character positioning.
x-axis
The x-axis is the horizontal line on the Cartesian plane. It runs left to right and is denoted as the x-axis. The center point where it meets the y-axis is called the origin, labeled as \(0,0\).
Values on the x-axis can be positive or negative:
  • Positive values are to the right of the origin.
  • Negative values are to the left of the origin.
For example, in the point \(4, -3\), \(4\) is the x-coordinate, which means moving 4 units to the right on the x-axis. Understanding the x-axis helps in correctly plotting the first coordinate of any point.
y-axis
The y-axis is the vertical line on the Cartesian plane. It runs up and down and is denoted as the y-axis. The y-axis intersects the x-axis at the origin \(0,0\).
Values on the y-axis can also be positive or negative:
  • Positive values are above the origin.
  • Negative values are below the origin.
For instance, in the point \(-2,-4\), \(-4\) is the y-coordinate, which means moving 4 units down from the origin. Understanding the y-axis is vital for correctly plotting the second coordinate of any point.
Points
Points are specific locations on the Cartesian plane. Each point is represented by a pair of coordinates \(x,y\). They help in visualizing data, solving geometric problems, and understanding graphs.
To plot a point, follow these steps:
  • Identify the x-coordinate and move accordingly on the x-axis.
  • Identify the y-coordinate and move accordingly on the y-axis.
  • The intersection of these moves is your point.
For example, the point \(-4,4\) is plotted by moving 4 units left on the x-axis and then 4 units up on the y-axis. Points give us a visual and spatial way to understand mathematical and real-world problems.

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