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Chapter 3: Problem 50

In which quadrant or on which axis is each point located? $$ (0,2.8) $$

Short Answer

Expert verified
The point \(0, 2.8\) is located on the y-axis.

Step by step solution

01

Identify the Coordinates

Observe the given coordinates which are \((0, 2.8)\). The first number in the pair is the x-coordinate and the second number is the y-coordinate.
02

Determine the X-Coordinate

The x-coordinate is \(0\). This indicates that the point is located directly on the y-axis because it does not move left or right from the origin.
03

Determine the Y-Coordinate

The y-coordinate is \(2.8\). This indicates that the point is \(2.8\) units above the origin on the y-axis.
04

Conclusion

Since the point does not move left or right from the origin and lies up on the y-axis, it is located 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
The coordinate plane is divided into four sections called quadrants. These quadrants are created by the intersection of two perpendicular lines: the x-axis (horizontal) and the y-axis (vertical). Each quadrant has a specific sign combination for coordinates:
  • Quadrant I: (+, +)
  • Quadrant II: (-, +)
  • Quadrant III: (-, -)
  • Quadrant IV: (+, -)
The point \((0, 2.8)\) lies directly on the y-axis since its x-coordinate is zero. Points that lie on the axes are not considered to be in any quadrant. Instead, they are simply on the axis.
X-Coordinate
The x-coordinate is the first number in an ordered pair \((x, y)\). It tells you how far to move left or right from the origin.
The x-coordinate can have three possible scenarios:
  • Positive: Move right from the origin.
  • Negative: Move left from the origin.
  • Zero: Do not move left or right.
In the exercise, the x-coordinate is \0\. This means the point does not move left or right from the origin. It stays directly on the y-axis.
Y-Coordinate
The y-coordinate is the second number in an ordered pair \((x, y)\). It tells you how far to move up or down from the origin.
The y-coordinate can have three possible scenarios:
  • Positive: Move up from the origin.
  • Negative: Move down from the origin.
  • Zero: Do not move up or down.
In the exercise, the y-coordinate is \2.8\. This means the point moves \2.8\ units up from the origin.
Origin
The origin is the point \((0,0)\) where the x-axis and y-axis intersect.
It is the reference point for all coordinates on the plane.
Here are some important points about the origin:
  • It represents the starting point for movement on the coordinate plane.
  • The coordinates \((0, y)\) or \((x, 0)\) indicate that the point lies on the y-axis or x-axis respectively.
  • All quadrants are defined relative to the origin. For any point, you first locate the origin and then move according to the x and y values.

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