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Chapter 2: Problem 8

The coordinate axes partition the \(x y\) -plane into four sections called ______.

Short Answer

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quadrants

Step by step solution

01

Identify the Coordinate Axes

The coordinate axes refer to the X-axis (horizontal axis) and the Y-axis (vertical axis) in the Cartesian plane.
02

Understand Partitioning

When the X-axis and Y-axis intersect, they divide the plane into four sections.
03

Naming the Sections

These four sections are known as quadrants. Specifically, they are Quadrant I (top-right), Quadrant II (top-left), Quadrant III (bottom-left), and Quadrant IV (bottom-right).

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Key Concepts

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

coordinate axes
In the context of the Cartesian plane, the coordinate axes are fundamental to understanding how points are positioned. They include the X-axis and the Y-axis. The X-axis runs horizontally across the plane, while the Y-axis runs vertically. These axes intersect at a point called the origin, which has coordinates (0,0). Understanding these axes is crucial because they serve as reference lines for locating points on the plane. To specify a point鈥檚 location, you provide its coordinates in the form (x, y), where 'x' is the distance along the X-axis and 'y' is the distance along the Y-axis.
quadrants
When the X-axis and Y-axis intersect, they divide the Cartesian plane into four sections known as quadrants. These quadrants help to identify the position of points on the plane. Each quadrant is numbered and located as follows:
  • Quadrant I: Top-right section where both x and y coordinates are positive (+,+).
  • Quadrant II: Top-left section where x is negative and y is positive (-,+).
  • Quadrant III: Bottom-left section where both x and y coordinates are negative (-,-).
  • Quadrant IV: Bottom-right section where x is positive and y is negative (+,-).
Knowing which quadrant a point is in helps to quickly determine the signs of its coordinates.
X-axis
The X-axis is the horizontal axis in the Cartesian plane. It serves as a reference line to measure horizontal distances. Points directly on the X-axis have their y coordinate equal to 0. For example, the point (3, 0) is 3 units to the right of the origin. If a coordinate x is positive, the point is to the right of the origin. If x is negative, the point is to the left of the origin.
Y-axis
The Y-axis is the vertical axis in the Cartesian plane. This axis is used to measure vertical distances. Points directly on the Y-axis have their x coordinate equal to 0. For instance, the point (0, 4) is 4 units above the origin. If a coordinate y is positive, the point is above the origin. If y is negative, the point is below the origin.

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