A Cartesian coordinate system specifies a point by its signed components along mutually perpendicular coordinate axes.
One of the straight lines through the origin parallel to a standard basis vector in a Cartesian coordinate system. The positive direction corresponds to positive values of that coordinate.
The point assigned all-zero coordinates in a chosen Cartesian coordinate system. Choosing an origin identifies position displacements with vectors; a bare affine space has no distinguished origin.
The two coordinate axes divide a Cartesian coordinate system in the plane into four open quadrants, distinguished by the signs of their coordinates. The positive quadrant is the first quadrant.
