Cambridge International Mathematics

Transformation geometry (Chapter 20) 413

b The object triangle OAB is mapped onto the image

triangle OAB^0.

Describe fully the single transformation which has

occurred.

c If ABCD is mapped onto A^0 B^0 C^0 D^0 , describe fully

the single transformation which has occurred.

d If ABCD is mapped onto A^0 B^0 C^0 D^0 describe fully the

single transformation which has occurred.

6 Find the image equation when:

a

b

c

Discussion Invariant points#endboxedheading

Invariant pointsare points which do not move under a transformation.

What points would be invariant under:

² a translation ² a rotation about O(0,0)

²²a stretch

² an enlargement or reduction about O(0,0)with scale factork?

In this section we consider the effect of transforming the graph ofy=f(x)intoy=f(x)+k,y=f(x+k)

and y=kf(x) where k 2 Z, k 6 =0.

Discovery

In this discovery we will graph many different functions. To help with this you can either

click on the icon and use the graphing package, or else follow the instructions on page

22 to graph the functions on your calculator.

F TRANSFORMING FUNCTIONS [3.8]

y

O x

A

B B'

3 6

y

O x

4

AB

1

1

24 8

DCD' C'

A' B'

y

O x

4 C'

A'

B' B

D

173

D' A

C

GRAPHING

PACKAGE

a reflection in a mirror line

y=2x is subjected to a stretch with invariantx-axis and scale factor k=3

y=^32 x is subjected to a stretch with invarianty-axis and scale factor k=^23

y=^12 x+2is subjected to a stretch with invariant line x=1and scale factor k=2.

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Y:\HAESE\IGCSE01\IG01_20\413IGCSE01_20.CDR Thursday, 30 October 2008 10:05:37 AM PETER