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Chapter 3: Problem 46

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

Short Answer

Expert verified
The point (6,0) lies on the x-axis.

Step by step solution

01

Identify the Coordinates

The point is given as (6,0). This means the x-coordinate is 6 and the y-coordinate is 0.
02

Determine the Location Based on Coordinates

Check the values of the coordinates. Since the x-coordinate is 6 and the y-coordinate is 0, the point 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 Cartesian coordinate system, the plane is divided into four sections called quadrants. These quadrants are created by the intersection of the x-axis and y-axis at the origin (0,0). Each quadrant is determined by the signs of the x and y coordinates of a point.

The quadrants are as follows:
  • First Quadrant - Both x and y coordinates are positive (x > 0, y > 0).
  • Second Quadrant - The x coordinate is negative, and the y coordinate is positive (x < 0, y > 0).
  • Third Quadrant - Both x and y coordinates are negative (x < 0, y < 0).
  • Fourth Quadrant - The x coordinate is positive, and the y coordinate is negative (x > 0, y < 0).

If a point is on either of the axes, it does not belong to any quadrant. In this case, with the point (6,0), it lies on the x-axis because the y-coordinate is 0.
axes
The x-axis and y-axis are the two perpendicular lines that form the basis of the Cartesian coordinate system:
  • The x-axis is the horizontal line where all points have a y-coordinate of 0. Points to the right of the origin have positive x values, and points to the left have negative x values.
  • The y-axis is the vertical line where all points have an x-coordinate of 0. Points above the origin have positive y values, and points below have negative y values.

These axes intersect at the origin (0,0), dividing the plane into the four quadrants mentioned earlier. When a point such as (6,0) lies on the x-axis, it means that the y-coordinate is 0 and the x-coordinate is a specific value, in this case, 6.
coordinates
Coordinates are a pair of numerical values \( (x,y) \) used to determine the precise location of a point on the Cartesian plane. The first value identifies the position along the horizontal x-axis, and the second value identifies the position along the vertical y-axis. Here's a breakdown of how to interpret coordinates:
  • x-coordinate (or abscissa) - Indicates how far left or right the point is from the origin. Positive values go right, and negative values go left.
  • y-coordinate (or ordinate) - Indicates how far up or down the point is from the origin. Positive values go up, and negative values go down.
For example, the point \( (6,0) \) has an x-coordinate of 6 and a y-coordinate of 0. This tells you to move 6 units to the right from the origin with no vertical shift, placing the point directly on the x-axis.

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