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Chapter 3: Problem 25

Answer the given questions. What is the \(x\)-coordinate of all points on the \(y\) -axis?

Short Answer

Expert verified
The x-coordinate is zero for all points on the y-axis.

Step by step solution

01

Identify properties of the y-axis

The y-axis is the vertical line in the Cartesian coordinate system where the x-coordinate of any point is zero. This is because it only moves up and down, not left or right.
02

Determine x-coordinate for points on the y-axis

Knowing that any point on the y-axis has an x-coordinate equal to zero, identify that this is a universal property of the y-axis regardless of the y-coordinate value.

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Key Concepts

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

Understanding the x-coordinate
In the Cartesian coordinate system, a point is represented by a pair of numerical values, often written as \(x, y\). These two numbers correspond to the \(x\)-coordinate and the \(y\)-coordinate, respectively. The \(x\)-coordinate indicates the position of the point along the horizontal axis, known as the x-axis.
It tells you how far the point is from the y-axis, which is the vertical line.
  • If the \(x\)-coordinate is positive, the point lies to the right of the y-axis.
  • If it is negative, the point is on the left side.
  • An \(x\)-coordinate of zero means the point is exactly on the y-axis.

In the context of points on the y-axis, the \(x\)-coordinate is specifically zero. This is a fundamental rule in coordinate geometry, making it easy to determine the x-coordinate for any point directly on the y-axis without further calculation.
Exploring the y-axis
The y-axis is a central concept in the Cartesian coordinate system. It is the vertical line that runs through the origin, where the x and y axes intersect, traditionally marked as the point \(0, 0\).
The y-axis plays a crucial role in plotting points since it helps in determining the vertical position of points.
Its main properties are:
  • The y-axis is perpendicular to the x-axis, forming a 90-degree angle.
  • All points on the y-axis have an \(x\)-coordinate of zero.
  • It stretches infinitely in both the positive (upwards) and negative (downwards) directions.
Understanding these properties can help you navigate and plot points effectively on a graph. The y-axis acts like a mirror line for graph symmetry in many mathematical functions.
Identifying points on the y-axis
Points on the y-axis are unique in the way they are described. Whenever you see a point with an x-coordinate of zero, you immediately know it lies on the y-axis. For instance, a point noted as \(0, 3\) means it is directly on the y-axis at a height of 3 units above the origin.
Similarly, \(0, -2\) is also on the y-axis, but 2 units below the origin.
  • These points don't move horizontally since their \(x\)-coordinate is zero.
  • Only the \(y\)-coordinate changes, which reflects their position up or down the y-axis.
The predictability of points on the y-axis makes them straightforward to identify and graph. Once you know the fundamental rule of the y-axis having \(x = 0\), you can easily determine the location of any such point.

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Most popular questions from this chapter

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