The Rectangular (Two-dimensional, Cartesian) Coordinate System
 
      Rectangular coordinate axes, x-axis and y-axis, origin, quadrants
      Ordered pair (x, y), coordinates of a point (abscissa x, ordinate y)
      Midpoint of a line segment
Rectangular coordinate axes, x-axis and y-axis, origin, quadrants
The Cartesian coordinate system is defined by two axes at right angles to each other, forming a plane.
The horizontal axis is labeled x, and the vertical axis is labeled y
The point of intersection, where the axes meet, is called the origin labeled O. 
Given each axis, choose a unit length, and mark off each unit along the axis, forming a grid. 
The position of each point in a plane is identified with an ordered pair of real numbers, in the form (x, y), called the coordinates of the point.
The x-coordinate, called the abscissa, equal to the distance of the point from the y-axis measured parallel to the x-axis, and the y-coordinate, called the ordinate, the distance of the point from the x-axis measured parallel to the y-axis.

The origin O has coordinates (0, 0).

   
The intersection of the two axes creates four quadrants indicated by numerals I, II, III, and IV. The quadrants are labeled counterclockwise starting from that in which both coordinates are positive.
Ordered pair ( x, y ), coordinates of a point (abscissa x, ordinate y)
On the Cartesian plane the points are placed as shown:
A( 3, 0 ),  B( 2, 3 ),  C( - 5/2, 4 ),  D( 0, 2 ), E( - 4, 0 ),  F( -2, -11/3 ),  G( 0, -1 ), and  H( 4, -2 ).
Midpoint of a line segment
The coordinates of the midpoint M(xM, yM) of the line segment AB where, A(x1, y1) and B(x2, y2) are endpoints:
   
Example:  Find the midpoint of the line segment AB where the endpoints, A(-5, 3) and B(-1, -1).
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