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Chapter 3: Problem 56

Plot and label each point in a rectangular coordinate system. $$ (0,-3) $$

Short Answer

Expert verified
Plot the point at (0, -3) and label it.

Step by step solution

01

- Identify the Coordinates

The point given is (0, -3). Here, 0 is the x-coordinate, and -3 is the y-coordinate.
02

- Locate the x-coordinate

Move along the x-axis to 0. Since the x-coordinate is 0, stay at the origin along the x-axis.
03

- Locate the y-coordinate

From the origin, move vertically downwards to -3 on the y-axis.
04

- Plot the Point

Place a dot at the position where the x-coordinate 0 and y-coordinate -3 meet. This is the point (0, -3).
05

- Label the Point

Write the coordinates (0, -3) next to the dot to label the point in the rectangular coordinate system.

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Key Concepts

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

Rectangular Coordinate System
The rectangular coordinate system, also known as the Cartesian coordinate system, is a two-dimensional plane used for graphing points, lines, and curves. It consists of two perpendicular lines called axes.

The horizontal line is the x-axis, and the vertical line is the y-axis. These axes intersect at a point called the origin, represented by \(0, 0\).

In this system, any point can be represented by an ordered pair \(x, y\). The x-coordinate tells you how far to move horizontally from the origin, and the y-coordinate tells you how far to move vertically.

This system is essential for plotting and visualizing mathematical functions and relationships.
Coordinates
Coordinates are a set of values that show an exact position on the rectangular coordinate system. Each point in the system is represented by an ordered pair \(x, y\).

Let's break down the coordinates:
  • x-coordinate: This value indicates the horizontal position of the point relative to the origin. Positive values are to the right of the origin, while negative values are to the left.
  • y-coordinate: This value indicates the vertical position of the point relative to the origin. Positive values are above the origin, while negative values are below.
For example, the point \(0, -3\) has an x-coordinate of 0 and a y-coordinate of -3. This means you don't move horizontally and move three units down from the origin to locate this point.
Graphing Points
Graphing points involves plotting the ordered pairs on the rectangular coordinate system. Here's how you can graph a point step-by-step:

  • Identify the Coordinates: Determine the x and y values from the given ordered pair.

  • Locate the x-coordinate: Move horizontally from the origin to the x-coordinate. If the x-coordinate is positive, move to the right; if it鈥檚 negative, move to the left.

  • Locate the y-coordinate: From the x-coordinate position, move vertically to the y-coordinate. If the y-coordinate is positive, move up; if it鈥檚 negative, move down.

  • Plot the Point: Place a dot where the x and y coordinates intersect.

  • Label the Point: Write the ordered pair next to the dot to identify it.
Using these steps, anyone can accurately plot points and graph them on the rectangular coordinate system.

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Most popular questions from this chapter

Find each quotient. $$ \frac{5-(-7)}{-4-(-1)} $$

Graph each linear equation. \(2 x+y=6\)

For each pair of equations, give the slopes of the lines and then determine whether the two lines are parallel, perpendicular, or neither. See Example \(6 .\) $$ \begin{aligned} &3 x-2 y=6\\\ &2 x+3 y=3 \end{aligned} $$

Graph each linear equation. \(6 x-5 y=18\)

For each pair of equations, give the slopes of the lines and then determine whether the two lines are parallel, perpendicular, or neither. See Example \(6 .\) $$ \begin{aligned} &2 x+5 y=4\\\ &4 x+10 y=1 \end{aligned} $$
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