View source for Affine coordinate system

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A rectilinear coordinate system in an [[Affine space|affine space]]. An affine coordinate system on a plane is defined by an ordered pair of non-collinear vectors  $  \mathbf e _ {1} $
and  $  \mathbf e _ {2} $(
an affine basis) and a point  $  O $(
the coordinate origin). The straight lines passing through the point  $  O $
and parallel to the basis vectors are known as the coordinate axes. The vectors  $  \mathbf e _ {1} $
and  $  \mathbf e _ {2} $
define the positive direction on the coordinate axes. The axis parallel to the vector  $  \mathbf e _ {1} $
is called the abscissa (axis), while that parallel to the vector  $  \mathbf e _ {2} $
is called the ordinate (axis). The affine coordinates of a point  $  M $
are given by an ordered pair of numbers  $  (x, y) $
which are the coefficients of the decomposition of the vector  $  \overline{OM}\; $
by the basis vectors:

$$ 
\overline{OM}\;  =  x \mathbf e _ {1} + y \mathbf e _ {2} .
$$

The first number  $  x $
is called the abscissa, while the second number  $  y $
is called the ordinate of  $  M $.

An affine coordinate system in three-dimensional space is defined as an ordered triplet of linearly-independent vectors  $  \mathbf e _ {1} , \mathbf e _ {2} , \mathbf e _ {3} $
and a point  $  O $. 
As in the case of the plane, one defines the coordinate axes — abscissa, ordinate and applicate — and the coordinates of a point. Planes passing through pairs of coordinate axes are known as coordinate planes.