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Chapter 9: Problem 33

For Exercises \(29-34\), plot the points on the rectangular coordinate system. $$(0,1)$$

Short Answer

Expert verified
Plot \(0,1\) by moving 1 unit up from the origin.

Step by step solution

01

Locate the Origin

Identify the origin of the rectangular coordinate system, which is the point \(0,0\).
02

Identify the Coordinates

The given point is \(0,1\). Notice that the first number is the x-coordinate and the second number is the y-coordinate.
03

Move Along the X-Axis

Since the x-coordinate is \(0\), do not move left or right from the origin.
04

Move Along the Y-Axis

From the origin, move 1 unit up because the y-coordinate is \(1\).
05

Plot the Point

Mark the point \(0,1\) on the coordinate plane.

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Key Concepts

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

Coordinate System
A coordinate system helps to locate points on a plane.
The most common type is the rectangular coordinate system.
This system is made up of two perpendicular lines called axes.
The horizontal axis is the x-axis, and the vertical axis is the y-axis.
Where these axes intersect is what we call the origin, labeled as \(0,0\).
Each point on this plane can be described using a pair of numbers, known as coordinates.
The first number is the x-coordinate, which tells us the position along the x-axis.
The second number is the y-coordinate, which shows the position along the y-axis.
X-Axis and Y-Axis
Understanding the x-axis and y-axis is crucial for plotting points.
The x-axis runs horizontally and represents values that can be positive (to the right of the origin) or negative (to the left of the origin).
The y-axis runs vertically and represents values that can be positive (above the origin) or negative (below the origin).
Each axis is a number line.
The point where the x-axis and y-axis cross is the origin.
To locate any point, always start from the origin.
The x-coordinate tells you how far to move left or right.
The y-coordinate tells you how far to move up or down.
Graphing Points
Graphing points is simple once you know how to read coordinates.
Let's take the point \(0,1\) from the exercise.
First, identify the x-coordinate and y-coordinate.
Here, the x-coordinate is \0\ and the y-coordinate is \1\.
From the origin, you would not move left or right because the x-coordinate is \0\.
Instead, you would move up 1 unit because the y-coordinate is \1\.
After moving, place a mark at that point on the graph.
That's how you plot the point \(0,1\). Remember, the first number tells you the horizontal movement, and the second number tells you the vertical movement.

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