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Chapter 2: Problem 23

In which quadrant or on which axis is each point located? \((-4.9,8.3)\)

Short Answer

Expert verified
Quadrant II

Step by step solution

01

- Understanding Quadrants and Axes

The coordinate plane is divided into four quadrants: Quadrant I (positive x and y), Quadrant II (negative x, positive y), Quadrant III (negative x and y), Quadrant IV (positive x, negative y). The axes are the x-axis and y-axis.
02

- Identify the Signs of Coordinates

Look at the coordinates \((-4.9, 8.3)\). The x-coordinate is -4.9 (negative) and the y-coordinate is 8.3 (positive).
03

- Determine the Correct Quadrant

According to the signs of the coordinates, negative x and positive y, the point \((-4.9, 8.3)\) falls in Quadrant II.

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Key Concepts

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

Quadrants in coordinate plane
The coordinate plane is a two-dimensional plane divided into four quadrants by the intersection of the x-axis and y-axis. These quadrants help us determine the position of points based on their coordinates.
  • Quadrant I: Both x and y coordinates are positive. For example, (3, 4).
  • Quadrant II: The x coordinate is negative while the y coordinate is positive. For instance, (-5, 2).
  • Quadrant III: Both x and y coordinates are negative, such as (-3, -7).
  • Quadrant IV: The x coordinate is positive while the y coordinate is negative, for example, (6, -1).
Understanding these quadrants is crucial to pinpointing precisely where a specific point lies on the coordinate plane.
x-axis and y-axis
The x-axis and y-axis are fundamental components of the coordinate plane. They form the basis for defining the location of points in this system.
The x-axis is a horizontal line that runs left to right. It represents the values for the x coordinates. For instance, a point at (3, 0) lies on the x-axis.
The y-axis is a vertical line that runs up and down. It represents the values for the y coordinates. A point at (0, 4) lies on the y-axis.
Points located directly on the axes do not belong to any quadrant. For example:
  • A point (4, 0) rests on the x-axis.
  • Similarly, a point (0, -3) sits on the y-axis.
Recognizing how the x-axis and y-axis function simplifies navigating the coordinate plane and determining point locations.
Points in coordinate system
Points in the coordinate system are specified by pairs of coordinates (x, y). Each pair indicates the exact position on the plane. Let鈥檚 break this down:
  • The x-coordinate shows how far left or right the point is from the y-axis. Positive values move right; negative values move left.
  • The y-coordinate shows how far up or down the point is from the x-axis. Positive values move up; negative values move down.
For an example, consider the point {-4.9, 8.3}:
  • The x-coordinate is -4.9, indicating the point is 4.9 units to the left of the y-axis.
  • The y-coordinate is 8.3, indicating the point is 8.3 units above the x-axis.
Together, these coordinates tell us that the point (-4.9, 8.3) is in Quadrant II, where x is negative, and y is positive. By understanding and applying these principles, you can easily find the location of any point in the coordinate system.

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