structural:scholar_edition, linguistic:voice_change, linguistic:paraphrasing
In two dimensions

Fixing or choosing the x -axis determines the y -axis up to direction. Namely, the y -axis is necessarily the perpendicular to the x -axis through the point marked 0 on the x -axis. But there is a choice of which of the two half lines on the perpendicular to designate as positive and which as negative. Each of these two choices determines a different orientation (also called handedness) of the Cartesian plane.

The usual way of orienting the plane, with the positive x -axis pointing right and the positive y -axis pointing up (and the x -axis being the "first" and the y -axis the "second" axis), is considered the positive or standard orientation, also called the right-handed orientation.

A commonly used mnemonic for defining the positive orientation is the right-hand rule. Placing a somewhat closed right hand on the plane with the thumb pointing up, the fingers point from the x -axis to the y -axis, in a positively oriented coordinate system.

The other way of orienting the plane is following the left-hand rule, placing the left hand on the plane with the thumb pointing up.

When pointing the thumb away from the origin along an axis towards positive, the curvature of the fingers indicates a positive rotation along that axis.

Regardless of the rule used to orient the plane, rotating the coordinate system will preserve the orientation. Switching any one axis will reverse the orientation, but switching both will leave the orientation unchanged.