2.1
Coordinate Plane
The coordinate plane, or Cartesian plane, is formed by two perpendicular number lines: a horizontal x-axis and a vertical y-axis.
These axes intersect at the origin—the point where both values are zero—dividing the plane into four labeled quadrants.
An ordered pair of coordinates represents every location in the plane. The first number indicates the position along the x-axis, and the second shows the position on the y-axis.
Coordinates function like an address system, uniquely identifying each point in the plane.
For example, a point with the coordinates (2, 3) lies two units to the right and three units above the origin.
All points with positive x-values lie to the right of the y-axis, and those with negative x-values lie to the left. A horizontal line represents points sharing the same y-value, and a vertical line shows points with the same x-value—whether positive or negative.
The coordinate system has real-world applications. For example, drones rely on it to follow precise flight paths and reach specific locations.
The Cartesian coordinate plane is a fundamental structure in mathematics that enables the visualization of relationships between numerical values in two dimensions. It is formed by two intersecting number lines: a horizontal x-axis and a vertical y-axis. These axes meet at the origin, the point where both values are zero. Their intersection divides the plane into four quadrants labeled in a counterclockwise direction starting from the upper right.
An ordered pair of numbers represents every point in the coordinate plane. The first number, the x-coordinate, indicates the position along the horizontal axis, while the second number, the y-coordinate, indicates the position along the vertical axis. These coordinates act like an address system, uniquely specifying each point's location. For example, the point with coordinates (2, 3) lies two units to the right and three units above the origin, located in the first quadrant. Negative x-values place points to the left of the vertical axis, while negative y-values place them below the horizontal axis.
Points sharing the same y-value lie along a horizontal line, and those with the same x-value lie along a vertical line. These lines can also serve as boundaries, defining specific regions of the plane. For instance, all points between two horizontal lines form a horizontal strip, while a vertical strip is formed between two vertical lines.
This system plots individual points, constructs geometric shapes, and analyzes data. It provides a foundation for various applications in mathematics, science, and technology, where spatial representation and precision are essential.
The coordinate plane, or Cartesian plane, is formed by two perpendicular number lines: a horizontal x-axis and a vertical y-axis.
These axes intersect at the origin—the point where both values are zero—dividing the plane into four labeled quadrants.
An ordered pair of coordinates represents every location in the plane. The first number indicates the position along the x-axis, and the second shows the position on the y-axis.
Coordinates function like an address system, uniquely identifying each point in the plane.
For example, a point with the coordinates (2, 3) lies two units to the right and three units above the origin.
All points with positive x-values lie to the right of the y-axis, and those with negative x-values lie to the left. A horizontal line represents points sharing the same y-value, and a vertical line shows points with the same x-value—whether positive or negative.
The coordinate system has real-world applications. For example, drones rely on it to follow precise flight paths and reach specific locations.
From Chapter 2:
Now Playing
2.1 : Coordinate Plane
Coordinates and Graphs
1.1K Views
2.2 : The Distance Formula
Coordinates and Graphs
930 Views
2.3 : The Midpoint Formula
Coordinates and Graphs
7.4K Views
2.4 : Graphs of Equations in Two Variables
Coordinates and Graphs
570 Views
2.5 : Circles
Coordinates and Graphs
413 Views
2.6 : Symmetry
Coordinates and Graphs
469 Views
2.7 : Solving Equations Graphically
Coordinates and Graphs
1.3K Views
2.8 : Solving Inequalities Graphically
Coordinates and Graphs
470 Views