In a Rectangular Cartesian System of coordinates the position of a point in a plane is determined by an ordered pair whose elements give the distances from the intersecting straight lines at right angles to each other. These lines are called the axes. The vertical line is called the Y-axis and the horizontal line is called X-axis. The meeting point O of the axes is called the origin. The distance measured along the X-axis is the x-coordinate or the abscissa. The distance measured along the Y-axis is called the y-coordinate or the ordinate.
The axes divide the plane into 4 quadrants and they are numbered in the anti-clockwise direction.
This system of rectangular Cartesian coordinates is named after the French Mathematician and Philosopher Rine Descartes (1596 - 1650).
The greatest modern mathematical tool available is relations and functions (analysis). Its usefulness is seen through emphasis on mathematising practical situations.Solving of problems depends on the ability to understand and apply mathematical analysis to different situations.
In this chapter, we will study some fundamental definitions and applications.
Ordered Pair
An ordered pair has a pair of elements which occur in a definite order.
If two ordered pairs (a, b) and (x, y) are equal, 
(a, b) = (x, y) then a = x, b = y.
Cartesian Product
Given two sets A and B. Then, all possible ordered pairs (x, y) obtained such that 
and 
is called the Cartesian product of the sets A and B.
Relations
If A and B are two non-empty sets, then a relation R in A x B is a subset of A x B. If we use the letter R to denote a relation, then we can write the relation between a and b as aRb a is related to b.
Representation of a Relation
Relations are Represented by:
(i) Roster form (ii) Set builder form (iii) By tables (iv) Arrow diagram (v) By graphs
Types of Relations
There are four types of relations as follows: (i) one - one (ii) many - one (iii) one - many (iv) many - many
Properties of Relations
Reflexive property: A relation R in a set A is said to be reflexive if every element of the set A is related to itself. This is if aRa where a Î A, or (a, a) Î R for each a Î A.
Transitive property: A relation R, is said to be transitive if a 'is related to' b and b 'is related to' c then a 'is related to' c, (a, b) 
R and 
if aRb, bRc then aRc.
Summary of Relation properties
(i) R is reflexive if aRa (ii) R is transitive if aRb and bRc implies aRc (iii) R is symmetric if aRb implies bRa.
Summary
An ordered pair has a pair of elements which occur in a definite order.
The four types of relation are: one-one, many-one, one-many and many-many.
