Y-coordinate

Definition

The y-coordinate is the vertical position of a point on a rectangular coordinate system. It represents the distance of a point above or below the x-axis, which is the horizontal axis. The y-coordinate is used in conjunction with the x-coordinate to uniquely identify the location of a point in the coordinate plane.

5 Must Know Facts For Your Next Test

1. The y-coordinate is always measured vertically, with positive values above the x-axis and negative values below the x-axis.
2. The y-coordinate, along with the x-coordinate, is used to uniquely identify the location of a point on the coordinate plane.
3. The y-coordinate is the second value in an ordered pair, with the x-coordinate being the first value.
4. The y-coordinate is essential for describing the vertical position of objects or data points in a variety of applications, such as graphs, maps, and engineering drawings.
5. Understanding the y-coordinate is crucial for performing operations and transformations on points in the rectangular coordinate system, such as translations, reflections, and rotations.

Review Questions

• Explain the role of the y-coordinate in the rectangular coordinate system.
  • The y-coordinate is a crucial component of the rectangular coordinate system, as it represents the vertical position of a point on the coordinate plane. Along with the x-coordinate, the y-coordinate is used to uniquely identify the location of a point. The y-coordinate is measured vertically, with positive values above the x-axis and negative values below the x-axis. Understanding the y-coordinate is essential for performing various operations and transformations on points in the coordinate system, such as translations, reflections, and rotations.
• Describe how the y-coordinate is used in conjunction with the x-coordinate to represent a point in the rectangular coordinate system.
  • In the rectangular coordinate system, a point is represented by an ordered pair (x, y), where the x-coordinate represents the horizontal position, and the y-coordinate represents the vertical position. The x-coordinate and y-coordinate work together to uniquely identify the location of a point on the coordinate plane. The y-coordinate is the second value in the ordered pair, and it is essential for describing the vertical position of objects or data points in a variety of applications, such as graphs, maps, and engineering drawings.
• Analyze the importance of the y-coordinate in the context of transformations and operations performed on points in the rectangular coordinate system.
  • The y-coordinate is crucial for performing various transformations and operations on points in the rectangular coordinate system. For example, when translating a point, the y-coordinate is used to determine the vertical shift of the point. Similarly, when reflecting a point across the x-axis, the y-coordinate changes its sign, while the x-coordinate remains the same. Additionally, the y-coordinate is essential for calculating the distance between two points and the slope of a line. Without a proper understanding of the y-coordinate and its role in the coordinate system, it would be challenging to accurately perform these fundamental operations and transformations.

Related terms

Rectangular Coordinate System: A two-dimensional coordinate system that uses perpendicular x and y axes to locate points in a plane. The x-axis represents the horizontal position, and the y-axis represents the vertical position.

Cartesian Coordinate System: Another name for the rectangular coordinate system, named after the mathematician and philosopher René Descartes, who developed this system.

Ordered Pair: A pair of numbers that represent the x-coordinate and y-coordinate of a point in the rectangular coordinate system, typically written as (x, y).