Explanation:
Cartesian coordinate system
Illustration
of a Cartesian coordinate plane. Four points are marked and labeled with their
coordinates: (2, 3) in green, (−3, 1) in red, (−1.5, −2.5) in
blue, and the origin (0, 0) in purple.
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. (Our solved example in mathguru.com
uses this concept)
Each reference line is called a coordinate
axis or just axis of the system, and the point where
they meet is its origin.
The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes,
expressed as signed distances from the origin.
Cartesian coordinates in two
dimensions
The modern Cartesian coordinate system in two dimensions (also
called a rectangular coordinate system) is defined by an ordered
pair of perpendicular lines (axes), a single unit of length for both axes, and an
orientation for each axis. (Early systems allowed "oblique" axes,
that is, axes that did not meet at right angles.) The lines are commonly
referred to as the x and y-axes where the x-axis is taken to be
horizontal and the y-axis
is taken to be vertical. The point where the axes meet is taken as the origin
for both, thus turning each axis into a number line.
The point where the axes meet is the common origin of the two
number lines and is simply called the origin.
It is often labeled O and if so then the axes are called Ox and Oy. A plane with x and y-axes
defined is often referred to as the Cartesian plane or xy plane. The value of x is called the x-coordinate or abscissa and the value of y is called the y-coordinate or ordinate.
Quadrants
The
four quadrants of a Cartesian coordinate system.
The axes of a two-dimensional Cartesian system divide the plane
into four infinite regions, called quadrants, each bounded by two
half-axes. These are often numbered from 1st to 4th and denoted by Roman numerals: I (where the signs of the two coordinates are I
(+, +), II (−, +), III (−, −), and IV (+, −). When the
axes are drawn according to the mathematical custom, the numbering goes counter-clockwise starting from the upper right ("northeast")
quadrant. (Our solved example in mathguru.com uses this concept).
http://en.wikipedia.org/wiki/Cartesian_coordinate_system
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