We know that, in analytical geometry of two dimensions the position of a point is determined w.r.t. two axes of reference.
But in the Space it is not possible to determine the point w.r.t. two axes.
Thus to locate the position of a point in Space another third axis is required besides the two axes.
Such a coordinate system in Space is called a three dimensional system.
 If xox1, yoy1 are two mutually perpendicular coordinate lines, intersecting at o then three exists a unique plane passing through these two lines.
 If zoz1 is a coordinate line perpendicular to this plane and passing through o then o is called origin.
 These three mutually perpendicular lines xox1, yoy1, zoz1 are called x - axis, y - axis, z - axis respectively.     

The plane passing through xox₁ and yoy1 is called xy - plane.
The plane passing through yoy₁ and zoz1 is called yz - plane
The plane passing through zoz₁ and xox1 is called zx - plane
              x - axis, y - axis and z - axis are called coordinate axes and the planes   xy  plane, 
yz - plane, zx - plane are called coordinate planes. Such a system of coordinate axes is called rectangular cartesian coordinate system.

Coordinate of a point in Space
Let P be any point in Space
Let A,  B,  C be the projections of P on X ,Y, Z coordinate axes.
Let x be the X - coordinate of A, y be the Y-coordinate of B and z be the Zcoordinate of C.
Then x,  y,  z are called the X,  Y,  Z coordinates of the point P and is denoted by the ordered trial, P  =  ( x,  y,  z ).

Let (  x,  y,  z )  be a given coordinate trial.
Let A be the point on X-axis with x as its X - coordinate, B be the point on Y - axis with y as its Y - coordinate and C be the point with z as its Z - coordinate on Z - axis.
Through the point A draw plane perpendicular to  . Now A will be the foot of the perpendicular drawn to   from any point in this plane. So x is the X - coordinate of any point in that plane.
Similarly, draw plane perpendicular to  and passing through B. Then y is Y - coordinate of every point in this plane.
Draw another plane passing through C and perpendicular to

. Every point on this plane will have z for its Z - coordinate.
These three mutually perpendicular lines intersect in a unique point P in Space and the coordinates of P are given by the ordered trial (x, y, z).
The three coordinate planes divide the Space into eight equal parts. Each part is called an Octant.
The signs of the coordinates of a point determine the octant in which it lies.
The following table shows the signs of the coordinates of points in the eight octants.