Problem 61 - College Algebra Essentials

Question

What is the rectangular coordinate system?

Step-by-Step Solution

Answer

Rectangular coordinate system, or Cartesian system, is a system that specifies each point uniquely in a plane (or space) by a pair (or a set) of numerical coordinates. The system has two perpendicular axes (x and y), four quadrants, and an origin at (0,0). Any point can be specified by an ordered pair of numbers (x, y).

Step 1: Define Rectangular Coordinate System

Rectangular coordinate system, also known as Cartesian coordinate system, is a two- or three-dimensional system in which the location of a point is specified by its distance along one or two perpendicular axes. The system was named after the French mathematician René Descartes.

Step 2: Explain the Components of Rectangular Coordinate System

In a 2D rectangular coordinate system, there are two axes: the horizontal (x-axis) and vertical (y-axis). They intersect at a point referred to as the 'origin', located at (0,0). These axes divide the plane into four regions, called 'quadrants'. Quadrant I is the upper right region, where both x and y have positive values. Quadrant II is the upper-left region (x is negative, y is positive), Quadrant III is lower-left (x and y are both negative) and Quadrant IV is lower-right (x positive, y negative).

Step 3: Demonstrate Representation of Points

In a rectangular coordinate system, any point in the plane can be represented by an ordered pair of numbers, (x,y). For example, the point (3, 4) represents the point at 3 units to the right of the origin along the x-axis, and 4 units above the origin along the y-axis. Similarly, a point like (-2, -3) represents movement of 2 units to the left of the origin and 3 units below it.