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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.

 

 

Index

Introduction

1.1 Functions And Mapping
1.2 Functions, Their Graphs and Classification
1.3 Rules for Drawing the Graph of a Curve
1.4 Classification of Functions
1.5 Standard Forms for the equation of a straight line
1.6 Circular Function and Trigonometry

Chapter 2





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