Problem 95 - Introductory Algebra for College Students

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 that is used to represent or plot points on a plane. It consists of two mutually perpendicular lines (the x-axis and y-axis) intersecting at the origin. A point is represented as (x, y), where x is the distance along the x-axis and y is the distance along the y-axis.

Step 1: Definition of rectangular coordinate system

The rectangular coordinate system, also known as the Cartesian coordinate system, is a two-dimensional system used to represent or plot points on a plane. It consists of two mutually perpendicular lines, known as the x-axis (horizontal line) and y-axis (vertical line), that intersect at a point called the origin.

Step 2: Graphical Representation

In the Cartesian coordinate system, any point is represented as \((x, y)\), where \(x\) is the distance measured along the x-axis and \(y\) is the distance measured along the y-axis. The \(x\) coordinate is called the abscissa and the \(y\) coordinate is called the ordinate.

Step 3: Plotting points in the rectangular coordinate system

To plot a point in this system, for example, \((2,3)\), start at the origin, move two units to the right along the x-axis for positive \(x\) value, and then move three units upwards along the y-axis for positive \(y\) value. The arrived point \((2,3)\) is the location of the point on the plane.