Rene Descartes invented the Cartesian coordinate system which relates points on a plane to pairs of real numbers. The system maps points onto a grid defined by perpendicular x and y axes, dividing the plane into four quadrants. Ordered pairs of real numbers (x, y) uniquely identify points by describing their position relative to the intersecting axes. For example, the point P is located at coordinates (2, 3) and point Q at (-5, -4).

1. ADVANCE ALGEBRA
Ms. Jerlyn A. Fernandez

2. RENE DESCARTES
• He is a French mathematician and philosopher who systematized the idea of
describing a point on the plane when he invented a system that relates the
correspondence between the points on a plane to a pair of real numbers.
• The system is called the Rectangular Coordinate System which later became
the Cartesian Coordinate System

3. THE CARTESIAN COORDINATE SYSTEM
y
Quadrant II
(-,+)
Quadrant I
(+,+)
x
Quadrant III
(-,-)
Quadrant IV
(+,-)

4. ORDERED PAIR
• Set of two well-ordered real number called coordinates
y
P ( 2, 3 )
The numerical
descriptive
reference of
point P is (2, 3)
x
Q ( -5 , -4 )
The numerical
descriptive
reference of point
Q is ( -5, -4)

5. PLOTTING OF POINTS
• Plot the following points on the same Cartesian plane then
determine their location.
1. O ( 5 , - 5 )
4. N ( 0 , 5 )
2. R ( - 4 , 3 )
5. E ( -5 , 0 )
3. I ( - 4 , - 4)
6. S ( 3 , 9/2 )

6. 1. O ( 5 , - 5 )
N
2. R ( - 4 , 3 )
S
R
3. I ( - 4 , - 4)
4. N ( 0 , 5 )
E
5. E ( -5 , 0 )
6. S ( 3 , 9/2 )
I
O

7.  EXERCISE:
State the coordinates for each point.
A
( 1, 5 )
C
( -3, 3 )
G
D
( 5, 2 )
E
I
( 0, 0 )
( - 4, 0 )
( 2, 0 )
F
J
( 1, - 2 )
( - 2, - 3 )
B
( -5, -5 )
H
( 2, - 5 )

8. RELATION
•
Association of an individual or object with another individual or object.
Definition of Relation
“A relation is any set of one or more ordered pairs.”

9. Using the elements of A =
1,2,3,4,5
,
construct the set of ordered pairs F that describes
the relation “The abscissa is one greater than the
ordinate”
F = (2,1), (3,2), (4,3), (5,4)

10.  EXERCISE
• From the set of numbers from 1 to 50
• Construct a set of ordered pairs that
shows the relation, “Each abscissa is a
square of each ordinate”.

11.  EXERCISE
• Construct a set of ordered pairs that
shows the relation, “The ordinate is two
more than the abscissa”.