Rectangular Coordinate System

Based on the sources, a Rectangular Coordinate System, also known as a Cartesian coordinate system, is a system used to specify each point in a plane by a set of numerical coordinates. It is important for studying algebraic properties of geometric objects such as points, lines, and planes. The system allows for the unique identification of a point on a plane.

Here are the key components and features of the rectangular coordinate system:

• Axes: The system uses two fixed perpendicular oriented lines measured in the same unit of length.
  • The horizontal line is called the X-axis. It allows movement from left to right.
  • The vertical line is called the Y-axis. It allows movement up and down.
  • The name “rectangular” comes from the fact that the two axes meet at a 90-degree angle (recta means right in Latin).
• Origin: The point where the two axes meet is called the origin, and its coordinate is (0, 0).
• Coordinates and Point Representation: Any point on the plane can be denoted by an ordered pair (x, y).
  • The first value, x, is the X-coordinate or abscissa, representing the distance travelled in the horizontal direction from the origin.
  • The second value, y, is the Y-coordinate or ordinate, representing the distance travelled in the vertical direction from the origin.
  • This ordered pair provides a precise description of the point’s location within the reference system. For example, to locate the point (3, 4), one travels 3 units in the horizontal direction and 4 units in the vertical direction. A negative x-coordinate means travelling to the left of the vertical line (Y-axis), and a negative y-coordinate means travelling below the horizontal line (X-axis).
• Quadrants: The coordinate axes split the coordinate plane into four quadrants and two axes. The quadrants are typically numbered in an anti-clockwise direction.
  • Quadrant I: Points in this quadrant have positive x and positive y coordinates (+, +).
  • Quadrant II: Points here have negative x and positive y coordinates (-, +).
  • Quadrant III: Points in this quadrant have negative x and negative y coordinates (-, -).
  • Quadrant IV: Points here have positive x and negative y coordinates (+, -).
  • Points that lie on the X-axis or Y-axis do not lie in any quadrant. On the X-axis, the y-coordinate is 0, and the x-coordinate can be positive or negative. On the Y-axis, the x-coordinate is 0, and the y-coordinate can be positive or negative. The origin (0,0) is also a special case.
  • Odd quadrants (I and III) have the same parity of x and y coordinates (both positive or both negative), while even quadrants (II and IV) have opposite parity. Understanding quadrants can help in graphing functions and points more effectively.

The rectangular coordinate system serves as a reference system to specify the location of a point in a specific manner and is fundamental to coordinate geometry.