Definition:Orientation of Coordinate Axes/Cartesian Plane

This page is about Orientation in the context of Analytic Geometry. For other uses, see Orientation.

Definition

There are $2$ different orientations of a Cartesian plane:

$\qquad \qquad \qquad$

Right-Handed

A Cartesian plane is defined as being right-handed if it has the following property:

Let a right hand be placed, with palm uppermost, such that the thumb points along the $x$-axis in the positive direction, such that the thumb and index finger are at right-angles to each other.

Then the index finger is pointed along the $y$-axis in the positive direction.

Left-Handed

A Cartesian plane is defined as being left-handed if it has the following property:

Let a left hand be placed, with palm uppermost, such that the thumb points along the $x$-axis in the positive direction, such that the thumb and index finger are at right-angles to each other.

Then the index finger is pointed along the $y$-axis in the positive direction.

Also known as

The orientation of a Cartesian coordinate system is known as it handedness.

The term arises from whether it is defined as a left-handed system or a right-handed system.

Sources

• 1936: Richard Courant: Differential and Integral Calculus: Volume $\text { II }$ ... (previous) ... (next): Chapter $\text I$: Preliminary Remarks on Analytical Geometry and Vector Analysis: $1$. Rectangular Co-ordinates and Vectors: $1$. Coordinate Axes