Cambridge International Mathematics

Transformation geometry (Chapter 20) 409

ENLARGEMENTS WITH CENTRE THE ORIGIN

Suppose P(x,y) moves to P^0 (x^0 ,y^0 )such that P^0 lies on the line OP, and OP^0 =kOP.

We call thisan enlargement with centre O(0,0)and scale factork.

From the similar triangles

x^0

x

=

y^0

y

=

OP^0

OP

=k

)

(

x^0 =kx

y^0 =ky

Under an enlargement with centre O(0,0)and scale factork, (x,y)!(kx,ky).

Example 8 Self Tutor

Consider the triangle ABC with vertices A(1,1),B(4,1) and C(1,4):

Find the position of the image of¢ABC under:

a an enlargement with centre O(0,0)and scale factor k=2

b a reduction with centre O(0,0)and scale factor k=^12.

ab

We can see from the examples above that:

If k> 1 , the image figure is anenlargementof the object.

If 0 <k< 1 , the image figure is areductionof the object.

EXERCISE 20D

1 Copy each diagram onto squared paper and enlarge or reduce with centre C and the scale factorkgiven:

abc

y

x

P(!'\\@)

P' ' '(! '\\@ )

y'

y

x x'

O

y

x

A

A' B

B'

C

C'

k=Qw_

5

O^5

y

x

A

A'

B

B'

C

C'

k=2

5

O^5

k¡=¡2

C

k¡=¡3

C

k¡=¡¡Qw_

C

IGCSE01

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(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_20\409IGCSE01_20.CDR Wednesday, 8 October 2008 4:13:51 PM PETER