
The Rectangular (Twodimensional,
Cartesian) Coordinate System 



Rectangular coordinate axes, xaxis
and yaxis,
origin, quadrants

Ordered
pair (x, y), coordinates of a point (abscissa x, ordinate y) 
Midpoint of a line segment






Rectangular coordinate axes, xaxis
and yaxis,
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
xcoordinate, called the
abscissa, equal to the distance of the point from the yaxis measured parallel
to the xaxis, and the
ycoordinate, called the
ordinate, the distance of the point from the xaxis measured parallel to the
yaxis.
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(x_{M},
y_{M})
of the line segment AB
where, A(x_{1},
y_{1})
and B(x_{2},
y_{2})
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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