Ms. Jerlyn A. Fernandez

ADVANCE ALGEBRA

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

THE CARTESIAN COORDINATE SYSTEMy

x

Quadrant IQuadrant II

Quadrant III Quadrant IV

( + , + )( - , + )

( - , - ) ( + , - )

ORDERED PAIR

y

x

Q ( -5 , -4 )

• Set of two well-ordered real number called coordinates

( 2, 3 )

The numerical descriptive reference of point P is (2, 3)

P

The numerical descriptive reference of point Q is ( -5, -4)

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 )

N S

R

E

I

O

1. O ( 5 , - 5 )

2. R ( - 4 , 3 )

3. I ( - 4 , - 4)

4. N ( 0 , 5 )

5. E ( -5 , 0 )

6. S ( 3 , 9/2 )

EXERCISE:State the coordinates for each point.

A

D

C

B

E

F

G

H

J

I

( 1, 5 )

( -5, -5 )

( -3, 3 )

( 5, 2 )

( 0, 0 )

( 1, - 2 )

( - 4, 0 )

( 2, - 5 )

( 2, 0 )

( - 2, - 3 )

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.”

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)

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”.

EXERCISE

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