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Chapter 2: Problem 22

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

Short Answer

Expert verified
Plot (3,0) by moving 3 units right on the x-axis from the origin.

Step by step solution

01

- Understanding the Coordinate System

A rectangular coordinate system consists of two perpendicular lines called axes: the x-axis (horizontal) and the y-axis (vertical). The point where they intersect is called the origin, denoted as (0,0). Each point is represented by a pair of numbers (x, y).
02

- Identifying the Coordinates

The point given is (3,0). The first number, 3, represents the x-coordinate and tells how far to move along the x-axis. The second number, 0, represents the y-coordinate and tells how far to move along the y-axis.
03

- Plotting the Point

Start at the origin (0,0). Move 3 units to the right along the x-axis since the x-coordinate is 3. Since the y-coordinate is 0, do not move up or down. Mark the point (3,0).

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Key Concepts

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

Coordinate Plane
The coordinate plane is like a giant grid used to locate points. Imagine it as a map where every location is marked by intersecting lines.
The plane is divided by two key lines:
  • x-axis: Runs horizontally from left to right.
  • y-axis: Runs vertically from top to bottom.
These axes intersect at the center, creating four areas called 'quadrants'.
Each point on the plane is found using a pair of numbers or coordinates. Coordinate pairs look like this: (x, y).
Knowing how to read and use the coordinate plane is super important for plotting points.
Plotting Points
Plotting points is like playing a game of connect-the-dots, but you mark only one point at a time!
Here's how you do it:
  • Start at the origin (0,0).
  • Look at the first number in your coordinate pair; this is the 'x' value. Move left or right along the x-axis by this amount.
  • Next, check the second number, the 'y' value. This tells you how much to move up or down the y-axis.
  • Once you've moved along both axes, you mark the spot!
For example, to plot the point (3, 0), you:
1. Start at (0,0).
2. Move 3 units to the right (since the x-value is 3).
3. The y-value is 0, so you don't move up or down.
You will end up marking the point at (3, 0). Simple, right?
x-axis and y-axis
The x-axis and y-axis are the foundations of the coordinate plane.
  • x-axis: This horizontal line runs left and right. Positive numbers are to the right of the origin, while negative numbers are to the left.
  • y-axis: This vertical line runs up and down. Positive numbers are above the origin, and negative numbers are below it.
The place where they meet, at (0, 0), is called the origin.
Think of them as a guide to finding any spot on the plane. The x-axis helps you move left or right, and the y-axis helps you move up or down.
Origin
The origin is the starting point on the coordinate plane. It鈥檚 like the (0, 0) spot on a treasure map!
Where the x-axis and y-axis intersect is the origin.
Here's why it's important:
  • It's the reference point for all coordinates.
  • Moving from the origin, you can find any other point.
So, when you鈥檙e plotting a point, you always begin at the origin.
For (3, 0), start at the origin, move right 3 spaces, and stay there because the y-value is 0.
This practice helps you understand distances and positioning on the plane.

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