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Chapter 2: Problem 21

In which quadrant or on which axis is each point located? \((0,-3)\)

Short Answer

Expert verified
The point \(0, -3\) is on the y-axis.

Step by step solution

01

Understand the Coordinate System

The coordinate system is divided into four quadrants. The horizontal axis is the x-axis, and the vertical axis is the y-axis. The origin \(0, 0\) is where these axes intersect.
02

Analyze the Provided Point

The point given is \(0, -3\). Here, the x-coordinate is 0, and the y-coordinate is -3.
03

Determine the Location Relative to the Axes

Since the x-coordinate is 0, the point must be on the y-axis. The y-coordinate of -3 indicates the point is located on the negative side of the y-axis.
04

Conclude the Point's Location

Given the characteristics discussed, the point \(0, -3\) lies on the y-axis.

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Key Concepts

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

quadrants
In a coordinate system, the plane is divided into four sections called quadrants. They help in determining the exact location of a point using x and y coordinates.
Each quadrant is numbered starting from the top-right and moves counterclockwise:
  • Quadrant I: Both x and y are positive
  • Quadrant II: x is negative, y is positive
  • Quadrant III: Both x and y are negative
  • Quadrant IV: x is positive, y is negative
Knowing which quadrant a point is in helps in understanding its position relative to other points and lines in the system.
axes
The axes in a coordinate plane are the two perpendicular lines that define the plane: the x-axis and the y-axis.
  • x-axis: The horizontal line. Points to the right of the origin have positive x-coordinates, and points to the left have negative x-coordinates.
  • y-axis: The vertical line. Points above the origin have positive y-coordinates, and points below the origin have negative y-coordinates.
These axes intersect at the origin and divide the plane into the four quadrants mentioned above. A point that lies directly on either the x-axis or the y-axis is not in any quadrant but on the line itself.
origin
The origin is the point where the x-axis and the y-axis intersect.
It is represented as \((0, 0)\). At this point, both coordinates are zero. The origin is the reference point for all other points on the plane.
When describing locations of points relative to the origin:
  • Positive x-coordinates are found to the right
  • Negative x-coordinates are found to the left
  • Positive y-coordinates are found above
  • Negative y-coordinates are found below
The origin acts as the central point and is crucial for understanding the layout of the coordinate system.

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