Cambridge International Mathematics

ANSWERS 713

ca translation of

¡¡ 3

0

¢

da translation of

¡ 0

2

¢

ea translation of

¡¡ 3

1

¢

fa 90 oanticlockwise rotation about O(0,0)

ga reduction, centre O(0,0), scale factor^14

han enlargement, centre O(0,0), scale factor 3

i a reflection iny=¡x

j a stretch with invariantx-axis and scale factor^23

ka reflection iny=¡ 2

l a stretch with invarianty-axis and scale factor 2

ma rotation about P, anticlockwise through 43 o

EXERCISE 20H

1a i ii

bi ii

cia 90 oanticlockwise rotation about O

ii a 90 oclockwise rotation about O

dia reflection in thex-axis ii a reflection in thex-axis

2a iT 3 ii T 3 iii T 6 iv T 0 vT 1

b

first

transformation

second transformation

T 0 T 1 T 2 T 3 T 4 T 5 T 6 T 7

T 0 T 0 T 1 T 2 T 3 T 4 T 5 T 6 T 7

T 1 T 1 T 0 T 3 T 2 T 5 T 4 T 7 T 6

T 2 T 2 T 7 T 4 T 1 T 6 T 3 T 0 T 5

T 3 T 3 T 6 T 5 T 0 T 7 T 2 T 1 T 4

T 4 T 4 T 5 T 6 T 7 T 0 T 1 T 2 T 3

T 5 T 5 T 4 T 7 T 6 T 1 T 0 T 3 T 2

T 6 T 6 T 3 T 0 T 5 T 2 T 7 T 4 T 1

T 7 T 7 T 2 T 1 T 4 T 3 T 6 T 5 T 0

REVIEW SET 20A

1a i(2,5) ii (¡ 5 ,2) iii (4,¡5)

bi(4,1) ii(5,4) c (2,2) d(6,¡2)

e(3,¡ 212 ) f (2^12 ,¡1)

2 (¡ 8 ,1)

3ay=2x¡ 9 by=¡ 2 x+1 c y=¡^12 x¡^12

dy=x¡ 1

4 Stretch with invariant line thex-axis and scale factork=^53.

7aa translation of

¡¡ 2

3

¢

ba reflection in the liney=¡x

ca stretch with invarianty-axis and scale factor^12

8aa reflection in they-axis ba reflection in thex-axis

REVIEW SET 20B

1a(3,2) b (2,¡3) c(3,10)

2a(¡ 5 ,¡11) b(¡ 7 ,¡3)

3a(9,15) b (¡ 4 ,3) c(¡ 5 ,¡ 112 )

4ay=¡ 2 x+6 bx+2y=1 c x¡ 2 y=¡ 1

d 2 x+2y=1

5 A stretch with invariant line they-axis with scale factork=3.

6a b

cd

7aA stretch with invariantx-axis and scale factork=2.

bg(x)=2f(x)

8aa reflection in thex-axis

ba rotation of 180 oabout O(0,0)

cA reduction about O(0,0)with scale factork=^13.

9aa reflection iny=x ba reflection iny=¡x

y

O x

A C

B

A' C'

B'

A"

B"C"

4

4

y

O x

A C

B'

B

C'

A"A'

B"C"

-3 3

3

y

O A C x

B

2468

2

4

6

8

A'

B'

C'

A"

C" B" yx¡=¡ y

O A C x

B

2468

2

4

6

8

A'

C' B'

yx¡=¡

A"

C" B"

5a b

cd

6

x

-4-2 2

22

y

yxx¡=¡¦()¡=¡2 ¡-¡1-4-4 yx¡=¡¦ ¡-¡2()

-2-2

O x

-4-2 2

22

-2-2

-4-4

y

yxx¡=¡¦()¡=¡2 ¡-¡1

yx¡=¡¦()¡-¡2

O

x

-4-2 2

22

y

yxx¡=¡¦()¡=¡2 ¡-¡1

-2-2yx¡=¡2¦()

-4-4

O x

-4-2 2

y

yxx¡=¡¦()¡=¡2 ¡-¡1

-2-2 yx¡=¡-¦()

-4-4

22

O

yxx¡=¡¦() \¡= ¡Qw_\¡+¡3

yx¡=¡-¦()

x

22

-8-8-6-6-4-4-2-2

44

22

-2-2

-4-4

y

x

22

44

22

y

yxx¡=¡¦() \¡= ¡Qw_\¡+¡3

yx¡=¡¦ ¡+¡1()

-8-8-6-6-4-4-2-2 O

x

22

y

yxx¡=¡¦() \¡= ¡Qw_\¡+¡3

yx¡=¡¦()¡+¡1

-8-8-6-6-4-4-2-2

44

22

O

x

22

44

22

y

yxx¡=¡¦() \¡= ¡Qw_\¡+¡3

yx¡= ¡ ¦\Qw_\ ( )

-8-8-6-6-4-4-2-2

O

O

y

x

yx¡=¡¦()

yx¡=¡¦()¡+¡3

()2 ¡6,

()2 -6,

()2 ¡3,

-2

1

4

4

yx¡=¡-2¦()

IB MYP_3 ANS

cyan magenta yellow black

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100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_an\713IB_IGC1_an.cdr Thursday, 20 November 2008 4:35:02 PM PETER