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Chapter 5: Problem 26

In Exercises \(21-32,\) indicate which quadrant contains the given point. If a point lies on one of the coordinate axes, indicate which one. $$(3,0)$$

Short Answer

Expert verified
The point (3,0) lies on the x-axis.

Step by step solution

01

Understand Coordinate Axes

The coordinate plane is divided into four quadrants by the x-axis and y-axis. The quadrants are labeled as Quadrant I (top-right), Quadrant II (top-left), Quadrant III (bottom-left), and Quadrant IV (bottom-right). Points on the axes do not belong to any quadrant.
02

Identify Point Location

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

Determine the Position

Since the y-coordinate is 0, the point \(3,0\) lies on the x-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 plane, we divide the plane into four areas known as quadrants. These quadrants help us locate points in a systematic way. Let鈥檚 explore the basic structure:
  • Quadrant I - Top-right section; here, both the x-coordinate and y-coordinate values are positive.
  • Quadrant II - Top-left section; here, the x-coordinate is negative and the y-coordinate is positive.
  • Quadrant III - Bottom-left section; in this quadrant, both x and y coordinates are negative.
  • Quadrant IV - Bottom-right section; here, the x-coordinate is positive and the y-coordinate is negative.
These quadrants are important in graphing and solving problems in coordinate geometry as they give us a way to categorize where points are located based on their signs.
X-axis
The x-axis is one of the two axes in the coordinate plane. It acts as a horizontal guideline, splitting the plane into the top and bottom halves. Here are some key points to know about the x-axis:
  • The x-axis is a horizontal number line.
  • Values on the right of the y-axis are positive.
  • Values on the left of the y-axis are negative.
At any point where the y-coordinate is zero, the point lies on the x-axis. For example, in our exercise, the point (3,0) lies on the x-axis because its y-coordinate is 0. The x-axis is crucial for determining if a point is located above, below, or directly on the horizontal reference line.
Y-axis
The y-axis complements the x-axis in creating a coordinate plane. It runs vertically and divides the plane into left and right halves. Key features of the y-axis include:
  • The y-axis is a vertical number line.
  • Values above the x-axis are positive.
  • Values below the x-axis are negative.
Points that have an x-coordinate of zero will lie on the y-axis. For example, a point such as (0,4) would lie on the y-axis since its x-coordinate is zero. Knowing how to identify points relative to the y-axis is crucial for graphing and solving various geometry problems.

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Most popular questions from this chapter

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