Coordinate systems: 
They are two mutually perpendicular coordinate lines which intersect in the origin O on each line.

The four quadrants in a coordinate system:
Quadrant I is the area where a>0 and b>0.
Quadrant II is the area where a<0 and b>0.
Quadrant III is the area where a<0 and b<0.
Quadrant IV is the area where a>0 and b<0.

Distance: 
The distance between any two points is defined as:
.

Data sets:
The grouping or collection of similar or related data.

Subsets:
If A and B are sets and every element of A is also an element of B, then: A is a subset of B, denoted by.

Product of two data sets:
If S and T are sets, the product set of S and T will be denoted by , which satisfies

.

Line:

A geometric figure formed by a point moving along a fixed direction and the reverse direction.

Slope of a line:
If and are arbitrary two points on the line, the slope can be calculated by
.

Midpoint of any two points:
The distance between two arbitrary points is given by
.

This tutorial describes the fundamental graphs of functions and how we graphically represent them in a Cartesian plane. Two dimensional coordinate systems are introduced with the assistance of graphs.

The midpoint, and the distance that is between two points are discussed in this tutorial. The graphical representation of data in a graph is introduced with the help of relations and the graphs of relations.

Specific Tutorial Features:

• Data sets, product of two data sets, and relations are introduced in this tutorial with step by step examples.
  
• The distance and midpoints between any two points  is found and presented with the use of graphs in some of the examples.

Series Features:

• Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
  
• Definition slides introduce terms as they are needed.
  
• Visual representation of concepts
  
• Animated examples—worked out step by step
  
• A concise summary is given at the conclusion of the tutorial.

Two dimensional coordinate systems
   Definition of coordinate systems
   Definition of the four quadrants
Distance and midpoint and their formulas
Relations
  Definition of data sets
  Subsets 
  The product of two data sets
  The relation of two data sets
Line in a plane
   Definition of a line
   Definition of the slope of a line
   Parallel and perpendicular lines