Cambridge International Mathematics

412 Transformation geometry (Chapter 20)

EXERCISE 20E

1 Copy these diagrams and perform the stretch with the given invariant line IL and scale factork:

ab

cd

2

ab

3 Find the image of:

a (3,¡1) under a stretch with invariantx-axis and scale factor 4

b (4,5)under a stretch with invariantx-axis and scale factor 2

c (¡ 2 ,1) under a stretch with invarianty-axis and scale factor^12

d (3,¡4) under a stretch with invarianty-axis and scale factor^32

e

4 Find the image of triangle ABC if A(1,2),B(4,1)and C(2,5)

a invariant line y=1and scale factor k=2

b invariant line x=¡ 1 and scale factor k=^12.

5aThe object rectangle OABC is mapped onto the image

rectangle OA^0 B^0 C^0.

Describe fully the single transformation which has

occurred.

IL

A B

C

k¡=¡2

IL

A

B

C

D

k¡= ¡Qw_

IL

P

Q

R

S k¡= 1¡Qw_ IL

X

Y

Z

W

k¡= ¡Qe_

y

x

O

2

IL

y¡=¡-2

P

Q

R

S

k¡=¡¡Qw_

4

y

x

O

x¡=¡1

IL

2

2

A

B

C

k¡=¡¡Ew_

y

O x

3

4 A

A'

B

B'

C

3 C'

(2,3) under a stretch with invariant line y=¡x and scale factor^12.

are its vertices as it is stretched with:

Copy and perform the stretch with given invariant line IL and scale factor :k

IGCSE01

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Y:\HAESE\IGCSE01\IG01_20\412IGCSE01_20.CDR Wednesday, 22 October 2008 1:34:35 PM PETER