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Chapter 4: Problem 59

In which quadrant or on which axis is \((-152,0)\) located? \(\quad[2.1]\)

Short Answer

Expert verified
Negative x-axis

Step by step solution

01

- Understand the Coordinates

A point in the coordinate system is given as \((-152, 0)\). The first value represents the x-coordinate and the second value represents the y-coordinate.
02

- Identify the Y-Coordinate

Notice that the y-coordinate is \(0\). Points where the y-coordinate is \(0\) always lie on the x-axis.
03

- Determine the Section of the Axis

Since the x-coordinate is negative \(-152, 0\), the point lies on the negative x-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 distinct regions known as quadrants. These quadrants are numbered from I to IV and are arranged in a counter-clockwise manner starting from the top right. Here鈥檚 how they are organized:

  • Quadrant I: Both x and y coordinates are positive (x, y).
  • Quadrant II: The x-coordinate is negative, and the y-coordinate is positive (-x, y).
  • Quadrant III: Both x and y coordinates are negative (-x, -y).
  • Quadrant IV: The x-coordinate is positive, and the y-coordinate is negative (x, -y).

Each quadrant helps in identifying the location of a point in the plane. In the given problem, since the y-coordinate is zero, the point does not fall into any quadrant but onto an axis.
Coordinate Plane
The coordinate plane, also known as the Cartesian plane, is a two-dimensional surface where any point can be defined with a pair of numbers. These numbers are known as coordinates and are written as (x, y). Coordinate planes have specific features:

  • Origin: The center point (0, 0) where the x-axis and y-axis intersect.
  • Positive and Negative Directions: The x-axis runs horizontally, with positive values to the right and negative values to the left. The y-axis runs vertically, with positive values upwards and negative values downwards.
  • Axes: The two lines that define the plane. The horizontal line is the x-axis and the vertical line is the y-axis.

Understanding these features is crucial because they help determine the exact position of any point, just like (-152, 0) in this exercise. Since the y-coordinate is zero, it means the point lies directly on the x-axis.
Axes
The coordinate plane consists of two main lines called axes. These axes are perpendicular to each other:

  • X-Axis: The horizontal line that determines the x-coordinate of a point. All points along the x-axis have a y-coordinate of zero.
  • Y-Axis: The vertical line that determines the y-coordinate of a point. All points along the y-axis have an x-coordinate of zero.

Points can lie on any of these axes. For example, (-152, 0) lies on the x-axis because its y-coordinate is zero. Specifically, it is on the negative side of the x-axis because the x-coordinate is -152. Remembering these details helps in quickly figuring out the location of a point on the coordinate plane.

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Most popular questions from this chapter

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