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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.
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