Problem 28 - College Algebra with Corequisite Support

Question

For each of the following exercises, identify the information requested. If a point is located on the \(y\) -axis, what is the \(x\) -coordinate?

Step-by-Step Solution

Answer

The x-coordinate is 0.

Step 1: Identify the Characteristics of the y-axis

The y-axis in a coordinate plane is a vertical line that passes through the origin. Any point located on the y-axis has an x-coordinate of 0.

Step 2: Conclusion

Based on the properties of the y-axis, a point on it will always have an x-coordinate of 0. Therefore, if a point is on the y-axis, its x-coordinate must be 0.

Key Concepts

x-coordinate

The x-coordinate plays a crucial role in coordinate geometry. It is the first value in an ordered pair \(x, y\). This value determines the location of a point along the horizontal axis of the coordinate plane.
The x-coordinate tells you how far left or right a point is from the origin. If the x-coordinate is zero, the point lies somewhere on the y-axis.

• Positive x-coordinates show that the point is to the right of the y-axis.
• Negative x-coordinates indicate a point to the left of the y-axis.
• When the x-coordinate is zero, the point directly aligns with the y-axis, indicating no horizontal displacement.

Hence, understanding the x-coordinate helps you figure out a point's horizontal position in the coordinate plane.

y-axis

The y-axis is one of the most important components of the coordinate plane. It is a vertical line running from top to bottom. This line passes through the origin and is symbolized by the letter "y."
In the coordinate plane, every point on the y-axis has an x-coordinate of zero. This means these points are exactly on the line with no horizontal shift.

• The y-axis divides the plane into two equal halves, known as quadrants.
• Points above the origin on the y-axis have positive y-values.
• Points below the origin have negative y-values.

Knowing about the y-axis helps understand the vertical positioning and symmetry in the coordinate system.

coordinate plane

The coordinate plane, also known as the Cartesian plane, is a two-dimensional flat surface used for plotting points, lines, and shapes. It is made up of two axes: the x-axis, which runs horizontally, and the y-axis, which runs vertically.
These two axes form a grid that allows us to represent geometric figures and algebraic relationships visually.

• Each point on this plane is identified uniquely by an ordered pair (x, y).
• The plane is divided into four quadrants, which help determine the signs of the x and y coordinates.
• The intersecting point of the axes is called the origin.

The coordinate plane is essential for solving various mathematical problems as it provides a visual representation of data.

origin

The origin is a fundamental reference point in the coordinate plane. It is the point where the x-axis and y-axis meet. Located at the coordinate (0, 0), the origin is the center of the coordinate plane.
It acts as a reference that helps define the positions of all other points within the plane.

• The origin defines the starting point for both axes, making it crucial for plotting and understanding coordinates.
• All distances on the coordinate plane are measured with respect to the origin.
• It's the only point that lies on both the x and y axes simultaneously.

The origin is a key concept for understanding the basic layout and calculations within the coordinate plane.