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Chapter 1: Problem 4

The intersection of the \(x\) -axis and the \(y\) -axis is the _____.

Short Answer

Expert verified
The origin

Step by step solution

01

Understand the x-axis

The x-axis is the horizontal line in a coordinate plane. All points on the x-axis have a y-coordinate of 0.
02

Understand the y-axis

The y-axis is the vertical line in a coordinate plane. All points on the y-axis have an x-coordinate of 0.
03

Determine the intersection

The point where the x-axis and y-axis intersect is where the x-coordinate and y-coordinate are both 0. This point is called the origin.

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Key Concepts

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

x-axis
Let's start with the x-axis. The x-axis is the horizontal line on a coordinate plane. Imagine it as a straight line that runs left to right. On this line, any point has a y-coordinate of 0.
For example, if you see a point like (5, 0) on the coordinate plane, it means the point is on the x-axis. The x-coordinate tells you how far to move left or right from the origin.
Remember, the x-coordinate can be positive or negative:
  • Positive numbers: Move to the right from the origin (e.g., (3, 0) is 3 units to the right).
  • Negative numbers: Move to the left from the origin (e.g., (-4, 0) is 4 units to the left).
Understanding the x-axis helps in plotting points and understanding their positions on the horizontal line.
y-axis
The next important concept is the y-axis. The y-axis is the vertical line on a coordinate plane. Picture it as a line that runs straight up and down. Any point on this line has an x-coordinate of 0.
For instance, a point like (0, 7) means the point is on the y-axis. The y-coordinate tells you how far to move up or down from the origin.
Remember, the y-coordinate can also be positive or negative:
  • Positive numbers: Move upwards from the origin (e.g., (0, 5) is 5 units up).
  • Negative numbers: Move downwards from the origin (e.g., (0, -6) is 6 units down).
Grasping the y-axis helps in understanding vertical positioning and plotting points accurately.
origin
Finally, let's talk about the origin. The origin is the point of intersection of the x-axis and y-axis.
It is represented by the coordinates (0, 0). This means both the x-coordinate and the y-coordinate are zero. Think of it as the 'home base' of the coordinate plane.
Any movement away from the origin can be described in terms of moving horizontally along the x-axis or vertically along the y-axis.
  • Examples: Moving 3 units right and 4 units up from the origin will give you the point (3, 4).
  • Or, moving 2 units left and 5 units down from the origin will give you the point (-2, -5).
The origin is crucial because it serves as the reference point for all other coordinates on the plane. Understanding it helps in precisely describing any point's location.

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