Problem 95 - Introductory and Intermediate Algebra for College Students 4th

Question

What is the rectangular coordinate system?

Step-by-Step Solution

Answer

The rectangular coordinate system is a method for labeling every point in a plane using an ordered pair of numbers, typically written as (x, y), where x is the horizontal position and y is the vertical position. This system includes the x-axis (horizontal line) and y-axis (vertical line) intersecting at a point called the origin (0,0). An example of its use would be plotting the point (2, 3) on the system by moving two units right from the origin (x-axis) and three units upwards (y-axis).

Step 1: Definition

The rectangular coordinate system—also known as the Cartesian coordinate system—provides a specific method for labeling every point in a plane or in three-dimensional space. This system uses an ordered pair of numbers or coordinates, written as \((x, y)\), where \(x\) represents the horizontal position and \(y\) represents the vertical position.

Step 2: Description of Components

This system consists of two number lines that intersect at a right angle. The horizontal line is called the x-axis and the vertical line is called the y-axis. The point at which these two axes intersect is called the origin and is denoted as (0,0). Both axes are divided equally and they can measure values positively (to the right or up) and negatively (to the left or down).

Step 3: Example

An example would be plotting the point (2, 3) on the rectangular coordinate system. Starting from the origin, move two units to the right along the x-axis (as \(x = 2\)), and then move three units upwards along the y-axis (as \(y = 3\)). The location arrived at is the representation of the point (2, 3) in the coordinate system.