PointsIn analytic geometry, a point is a singular position within a specific coordinate system. A point is a dimensionless contstruct, in that it does not have size or shape of any sort. Because a point is dimensionless, it can exist in any coordinate system with any number of dimensions. A point (sometimes called a position vector) in a Cartesian coordinate system is represented by either two values (planar) or three values (spacial), and are specified as an ordered set. They are called ordered because they are always specified in a predefined order. For example, a planar point is generally specified as (x, y), and a spacial point is generally specified as (x, y, z). Each value represents the linear distance from the point to zero along the axis line. This is the same as saying that it is the distance from the point to its perpendicular axis (x is perpendicular to the y-axis, and y is perpendicular to the x-axis.) These values are known as the x- and y- intecepts. For example, the planar point (5,2) is 5 units up from the x-axis and 2 units right of the y-axis. The point at zero of the coordinate system (0,0) or (0,0,0) is generally refered to as the origin of the coordinate system. |
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Analytic Geometry: Introduction | Analytic Geometry: Lines |