Problem 49 - College Algebra

Question

What is the rectangular coordinate system?

Step-by-Step Solution

Answer

The rectangular coordinate system, also known as the Cartesian coordinate system, is a two-dimensional system in which the position of a point is defined by its distances from two intersecting lines (x and y axes). Each point in this plane can be represented as an ordered pair \((x, y)\), where 'x' is the horizontal distance and 'y' is the vertical distance from the origin.

Step 1: Definition of the Rectangular Coordinate System

The rectangular coordinate system is a two-dimensional system of coordinates in which the position of a point is specified by its distance from two intersecting lines known as axes (x and y). This system is also known as the Cartesian coordinate system.

Step 2: Components of the Rectangular Coordinate System

The two intersecting lines in the rectangular coordinate system are known as the x-axis (horizontal line) and the y-axis (vertical line). These axes intersect at a point known as the origin, typically symbolized by the letter 'O'. Each point in this plane can be represented as an ordered pair \((x, y)\) where 'x' denotes the horizontal displacement and 'y' the vertical displacement from the origin.

Step 3: Using the Rectangular Coordinate System

Points in the plane are located relative to the origin, 'O' along two perpendicular directions, that is, up or down (along the y-axis) and left or right (along the x-axis). Each point in the plane is associated with a pair of such numbers, called coordinates, which are in fixed one-to-one correspondence with the points in the plane.