Cambridge International Mathematics

402 Transformation geometry (Chapter 20)

Many trees, plants, flowers, animals and insects

aresymmetricalin some way. Such symmetry

results from a reflection, so we can describe

symmetry using transformations.

Intransformation geometryfigures are changed

(or transformed) in size, shape, orientation or

position according to certain rules.

The original figure is called theobjectand the new figure is called theimage.

We will consider the followingtransformations:

² Translationswhere every point moves a fixed distance in a given direction

² Reflectionsor mirror images

² Rotationsabout a point throught a given angle

² Enlargementsandreductionsabout a point with a given factor

² Stretcheswith a given invariant line and a given factor.

Here are some examples:

translation (slide) reflection

rotation aboutOthrough angleμ enlargement

reduction (k=^12 ) stretch

Click on the icon to obtain computer demonstrations of these transformations.

Atranslationmoves an object from one place to another. Every point on the object moves the same distance

in the same direction.

A TRANSLATIONS [5.4]

mirror line

image object

object image

O centre object image

object

image

q

COMPUTER

DEMO

object

image

centre

object

k=^12 k=2

invariant

line

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_20\402IGCSE01_20.CDR Wednesday, 22 October 2008 1:32:10 PM PETER