2
2
two
The coordinates of the point satisfy each of the equations.
Correct.
In a two-axis system, each point has coordinates that specify its position in relation to the two axes. The horizontal axis is typically labeled x, and the vertical axis is labeled y. The coordinates of a point are written as (x, y).
The coordinates of a point in the n-space are ordered sets of n numbers, each of which measures the distance of the point from the origin along the n-axes in a given order.
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis of the system.
We assume that the ambient space is equipped with the standard Cartesian coordinate system and specify points by their Cartesian coordinates.The Cartesian coordinates of a point in the plane are a pair (x,y).The homogeneous coordinates of a point in the plane are a triple (x,y,w) with w!=0. The Cartesian coordinates of a point with homogeneous coordinates (x,y,w) are (x/w,y/w).Remark: We notice that the homogeneous coordinates of a point are not unique. Two triples that are multiples of each other specify the same point.The Cartesian coordinates of a point are of type double in the floating point kernel and of type rational in the rational kernel. The homogeneous coordinates of a point in the rational kernel are of type integer. Points in the floating point kernel are stored by their Cartesian coordinates.For points in the rational kernel it is more efficient to store them by their homogeneous coordinates, i.e., to use the same denominator for x- and y-coordinate.For compatibility also points in the floating point kernel have homogeneous coordinates (x,y,1.0). These homogeneous coordinates are of type double.
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates. These coordinate system can be used to provide geometric interpretations for many branches of mathematics.
So that when discussing a number of points, the coordinates of each point can be clearly distinguished from one another.
For Cartesian coordinates in n-dimensional space there are n axes which are [usually] orthogonal and which meet at a single point called the origin. The coordinates of any point in the n-space are defined by ordered n-tuples whose terms refer to the distances of the point, from the origin, along each of the axes.