Koordinataxlar

Koordinataxlar, or coordinate axes, are the reference lines in a coordinate system used to specify the position of points by coordinates. They form a framework that defines directions and units, allowing for the description of space in two or three dimensions. The lines typically intersect at a single point called the origin, which serves as the zero reference for all coordinates.

In two dimensions, the coordinate axes are the x-axis and the y-axis. A point in the plane is denoted by (x, y), where x measures distance along the x-axis from the origin and y measures distance along the y-axis. The axes are usually taken to be perpendicular, with positive x directed to the right and positive y directed upward. The axes provide a basis for representing vectors as linear combinations of unit vectors along each axis.

In three dimensions, a third axis, the z-axis, is added. Points are written as (x, y, z). The orientation of the three axes can follow different conventions, commonly described as right-handed or left-handed coordinate systems. In a right-handed system, rotating from the x-axis toward the y-axis points in the direction of the z-axis; the exact orientation depends on the chosen convention, which affects signs in calculations and transformations.

Koordinataxlar underpin many mathematical constructs, including vector spaces where the axes form a basis. They are essential for performing translations, rotations, scaling, and projections, and for describing planes, lines, and surfaces through equations. They appear in physics, computer graphics, engineering, geography, and many applied fields.

Historically, the Cartesian coordinate system, introduced by René Descartes, linked algebra and geometry through koordinataxlar, enabling algebraic methods to express geometric relationships.