Example 9
If f (x) = x  x^{1} show that f
=  f (x)
Solution :
f (x) = x
\ f
=

=
 x
\ f
= 
=  f (x) \
f
=  f (x)
Example 10
Find the slope of the line joining A(2, 3) and B (5,7).
Solution :
m = =
=
=
Example 11
Show that the points A (2,2), B(3,4) and C (4,1) are the vertices
of a right angled triangle.
Solution :
Here slope of segment AB = = 2
slope of segment BC = = 3
and slope of segment AC =
=
\ (slope of segment AB) (slope of segment AC)
= 2 = 1
\ segment AB is perpendicular to segment AC
\ triangle ABC is a right angled at A.
Example 12
Show that A ( 3, 1 ), B (1, 9) and C ( 4,  1 ) are collinear points.
Solution :
slope of segment AB = = = 2
slope of segment BC = = = 2
Since slope of segment AB = slope of segment BC and B is common to both lines, segment AB and segment BC belong to the same line. Hence A, B and C are collinear points.
