Cartesian Coordinate System

Overview

In plane analytic geometry, the Cartesian coordinate system in a plane uniquely specifies coordinates using a pair of real numbers. These coordinates represent signed distances to the point from two fixed perpendicular oriented lines called the axes. The point where the axes meet is called the origin and has coordinates $⟨0,0⟩$.

An equation that completely characterizes a figure within the Cartesian coordinate system is called a Cartesian equation.

Transformations

There are two kinds of transformations that we can do to a graph: shifting and scaling. A reflection is a special case of scaling.

Shifting

A vertical shift adds/subtracts a constant to every $y$-coordinate of a graph, leaving the $x$-coordinate unchanged. A horizontal shift adds/subtracts a constant to every $x$-coordinate of a graph, leaving the $y$-coordinate unchanged.

Scaling

A vertical scaling will multiply/divide every $y$-coordinate of a graph, leaving the $x$-coordinate unchanged. A horizontal scaling will multiply/divide every $x$-coordinate of a graph, leaving the $y$-coordinate unchanged.

Scaling is also known as stretching and compressing.

Reflecting

A reflection is a special case of a scaling.