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Chapter 2: Problem 22

In which quadrant or on which axis is each point located? \((6,0)\)

Short Answer

Expert verified
On the positive x-axis.

Step by step solution

01

- Identify the Coordinates

Identify the coordinates of the point given. Here, the point is \(6,0\). The first number represents the x-coordinate and the second number represents the y-coordinate.
02

- Analyze the Coordinates

Analyze the values of the coordinates. If the x-coordinate is positive, it means the point is to the right of the y-axis. If the y-coordinate is zero, the point lies on the x-axis.
03

- Determine the Location

Since the x-coordinate is positive and the y-coordinate is zero, the point \(6,0\) is located on the positive x-axis.

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Key Concepts

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

Quadrants
In coordinate geometry, the plane is divided into four parts called quadrants. These are created by the intersection of the x-axis and y-axis.
Each quadrant has its own characteristics:
  • Quadrant I: Both x and y coordinates are positive.
  • Quadrant II: x-coordinate is negative, and y-coordinate is positive.
  • Quadrant III: Both x and y coordinates are negative.
  • Quadrant IV: x-coordinate is positive, and y-coordinate is negative.
Understanding which quadrant a point lies in helps in visualizing and solving geometry problems.
For example, the point (6,0) lies on the x-axis, not in any quadrant since its y-coordinate is zero.
X-Axis
The x-axis is the horizontal line in a coordinate plane. Points along this line have a y-coordinate of zero. The x-axis divides the plane into the upper and lower halves.
When labeling points on the x-axis:
  • If x is positive, the point lies to the right of the origin (0,0).
  • If x is negative, the point lies to the left of the origin.
In the example provided, the point (6,0) lies on the positive x-axis, precisely 6 units to the right of the origin.
This means the y-coordinate is zero, and the point does not move up or down from the origin.
Y-Axis
The y-axis is the vertical line in a coordinate plane. Points along this line have an x-coordinate of zero.
The y-axis divides the plane into the left and right halves.
  • If y is positive, the point lies above the origin.
  • If y is negative, the point lies below the origin.
Points on the y-axis do not have horizontal movement. When analyzing points such as (6,0), note that the x-coordinate is not zero, so it does not lie on the y-axis. It is always important to distinguish between the x-axis and y-axis when determining the location of a point.
Coordinates
Coordinates describe the position of a point on a coordinate plane. They are written as (x,y), where x is the horizontal value, and y is the vertical value.
Some important aspects of coordinates include:
  • The x-coordinate indicates horizontal distance from the origin.
  • The y-coordinate indicates vertical distance from the origin.
  • If both coordinates are zero, the point is at the origin.
  • If one coordinate is zero, the point lies on one of the axes.
For instance, in the point (6,0), the x-coordinate is 6, and the y-coordinate is 0.
This tells us the point is on the x-axis, and exactly 6 units to the right of the origin.

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