8.2 Relations, Graphs and symmetry
1) A relation is a set of ordered pairs of numbers. Relations are usually written in the
set builder notation.
For example {(x, y)  y £ x}, { (x, y)  y = x^{2} + 1 } etc.
In most cases we just write y £ x, y = x^{2} + 1 etc.
Many a times we just give the list of ordered pairs { (1,2) , (3,5), (2,6) }
A relation can be best understood by sketching its graph.
First, we will study graphic equations on the coordinate plane.
To graph an equation on the coordinate plane, find the solutions by giving a value to one variable and this will help solve the other variable. Then graph the solutions.
Example Find the distance of the point A(3,4) from 0 [origin].
Solution : A (x_{1}, y_{1}) = ( 3, 4 )
Distance of A from the origin 0, is
Example Find the distance between the points (2,3) and (7,8)
Solution : Let A (x_{1}, y1) = (2, 3) and B (x_{2} , y_{2}) = (7, 8)
Distance between points A and B, is.
Example The distance between the point A (8,8) and a point B on the y  axis is 10.
Find the Coordinates of B.
Solution : Since point B is on the yaxis, B is (0, y_{2})
Let A (x_{1}, y_{1}) = (8, 8)
The distance between A and B, is
