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ANSWERS

Chapter 26

Exercise 26A

1 a b c

d

e f

2

3 a

b

4 a, b

c d

Exercise 26B

1

2 a, b, c

3 a i rotation of 90 anticlockwise about (0,0) or a quarterturnclockwise about (0, 0)ii rotation of 180 about (0, 0) or a half turn about (0, 0)

iii rotation of 90 clockwise about (0, 0)b rotation of 90 clockwise about (0, 0)c rotation of 180 about (0, 0)

4 a i rrotation of 180 about (3, 5)ii rotation of 90 clockwise about (2, 1)

iii rotation of 180 about (0, 0)iv rotation of 90 anticlockwise about (0, 4)v rotation of 90 anticlockwise about (2, 2)

b rotation of 90 clockwise about (2, 8)

c i translation with vector ii translation with vector

Exercise 26C

1 a b

40

610

O 1 2 3 4 5 66 5 4 3 2 1

2

1

4

3

6

5

5

6

43

2

1

Q

P

R

S

O 1 2 3 4 5 66 5 4 3 2 1

2

1

4

3

6

5

5

6

4

3

2

1

A

CB

D

2

4

24

O 1 2 3 4 55 4 3 2 1

2

1

4

3

6

5

5

4

32

1

A

C

B

53

O 1 2 3 4 55 4 3 2 1

2

1

5

4

32

1A

O 1 2 3 4 5 6 7 8 9 105 4 3 2 1

5

4

3

2

1

7

8

6

5

4

3

21

A

G E

B

C

F

D

2

52

3

0

4

5

0

2

465

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ANSWERS

c d

2 a

b c

3 a, b

c a reflection in y 14 a, b

c a reflection in y x d a rotation of 180 about (0, 0)

Exercise 26D

1 length 8cm, width 6cm

2

3 4 cm, 3 cm

4

5 a, b

6 a 4 b 3 c 112 d 12 e 8 f 18

7 a

b i 12 cm ii 24 cm iii 36 cmc i 8 cm2 ii 32 cm2 iii 72 cm2

d i 2 ii 3 Values are the same as the scale factorse i 4 ii 9 Values are the same as the squares ofthe scale factors

P

Q

R

AB

C

5

6

4

3

2

1

1

O

2

3

4

5

6

y

56 4 3 2 1 1 2 3 4 5 6x

B

A

C

5

6

4

3

2

1

1

O

2

3

4

5

6

y

56 4 3 2 1 1 2 3 4 5 6x

P

R

Q

T

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ANSWERS

Exercise 26E

1 a b

c d

2 a, b, c, d ii

e i scale factor 6

Note the centre of enlargement is (4.4, 1)

3 a Enlargement centre (0, 0) scale factor 3

b Enlargement centre (4, 2) scale factor 2

c Enlargement centre (4, 2) scale factor 12

4

5

6 a Enlargement with scale factor 4,centre (9, 5)

b Enlargement with scale factor 14, centre (9, 5)

4

3

2

1

1

O

2

3

4

5

6

7

8

9

y

1 2 3 4 5 6 7 8 9 10 x

P

Q

R

4

3

2

1

1

O

2

3

4

5

6

7

8

9

10

y

1 2 3 4 5 6 7 8 9 10 11 12 x

P

Q

R

5

8

4

3

2

1

1

O

2

3

4

5

6

6

7

7

8

9

10

y

58 4 3 2 1 1 2 3 4 5 66 77 8 x

A

C

B

Q

R

P

a

b

c

iii

ii

ii

ii

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ANSWERS

Exercise 26F

1 a, b

c Rotation of 180 about (0, 0)

2 a, b

c Reflection in the line x 4

3 a, b

c Translation with vector

4 a, b

c Reflection in the line x 4

5 a, b

c Rotation of 90clockwise about (5,1)

6 a, b

c Reflection in the line y x

5

4

3

2

1

1

O

2

3

4

5

y

5 4 3 2 1 1 2 3 4 5x

P

Q

R

y x

y x

O

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10

y

P

Q

R

x

5

4

3

2

1

1

O

2

3

4

5

y

1 2 3 4 5 6 7 8x

CA

B

y x

80

O

1

2

3

4

5

6

1 2 3 4 5 6 7 8 9 10 11 12

yx 3 x 7

T U V

x

5

4

3

2

1

1

O

2

3

4

5

y

1 2 3 4 5 6 7 8 9x

PR

Q

y

5

4

3

2

1

1

O

2

3

4

5

y

5 4 3 2 1 1 2 3 4 5x

P

QA

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ANSWERS

c

d

e

f

g

h

i

j

5

4

3

2

1

1

O

2

3

4

5

y

5 4 3 2 1 1 2 3 4 5x

5

4

3

2

1

1

O

2

3

4

5

y

5 4 3 2 1 1 2 3 4 5x

5

4

3

2

1

1

O

2

3

4

5

y

5 4 3 2 1 1 2 3 4 5x

5

4

3

2

1

1

O

2

3

4

5

y

5 4 3 2 1 1 2 3 4 5 x

5

4

3

2

1

1

O

2

3

4

5

y

5 4 3 2 1 1 2 3 4 5x

5

4

3

2

1

1

O

2

3

4

5

y

5 4 3 2 1 1 2 3 4 5x

5

4

3

2

1

1

O

2

3

4

5

y

5 4 3 2 1 1 2 3 4 5x

5

4

3

2

1

1

O

2

3

4

5

y

5 4 3 2 1 1 2 3 4 5 x

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ANSWERS

k

l

m

n

o

2 a x 2y 4, 2y x, x 1b x 2y 4, 2y x, x 1 c 2

3 a b c (2, 1) (2, 2)

4 b 3y 2x 12, x 1, y 1 c (2, 2) (3, 2)5 a x 3, y 6

b

c (1, 1), (1, 2) (0, 0) (0, 1) (0, 2) (1, 2)6 a For example x 0, y 5 and x 2, y 2

b

O

2

4

6

2 4 6

y

x

6x 5y 30

y 1

2xy

2

1

O

1

2

3

4

5

6

7

8

1

1

2 2 3

y

x

xy1

y 2x

yx 3

2y 5

3

2

1

O

1

2

3

4

5

6

7

1 2 3

y 2x 3

2xy 6

x 1

y

x

5

4

3

2

1

1

O

2

3

4

5

y

5 4 3 2 1 1 2 3 4 5 x

5

4

3

2

1

1

O

2

34

5

y

5 4 3 2 1 1 2 3 4 5x

5

4

3

2

1

1

O

2

3

4

5

y

5 4 3 2 1 1 2 3 4 5x

5

4

3

2

1

1

O

2

3

4

5

y

5 4 3 2 1 1 2 3 4 5x

5

4

3

2

1

1

O

2

3

4

5

y

5 4 3 2 1 1 2 3 4 5 x

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ANSWERS

Chapter 28

Exercise 18A

1 40

2 a T 39 b T 8

3 a m 3.5 b m 3.

4 a v 35 b v 6 c v 365 a F 86 b F 32 c F 40

6 a x 3 b x 6

7 a 48 b 76

8 a 120 b 175

9 a T 110 b T 80

10 a d 60 b d 33 c d 68

11 6.95

12 100.8

Exercise 28B

1 C 40t 30d2 N e b where N total number of apples, e eating,

b baking

3 a C 30t 75b 285 where C total cost, in , t number of days

4 a P 3sb 15 m where P perimeter, s length of each side

5 a T pt b b T 210

6 a C 1.5n 2s b C 12

7 x m

3

e s where m maths %, e English %,

s science %

8 a T b(p 8)b i T 408

ii A total of 408 passengers can travel on 6 buses

Exercise 28C

1 a x y 7 b x 4

y c x

y

2

1

d x y

3

5 e x 1 y f x

6

2

y

2 w A

l 3 t

s

u

u2 4 m

3n

2

W.

5 a u v at b a v

t

u c t

v

a

u

6 a P D

3

3Q b P

D

8

12Q c P

10Q

2

D

7 a 3c b 8 f2g

3

e

9 n 5b

1

5

2a 10 r

A

11 a u v2 2as b 12

Exercise 28D

1 a identity b formula

c identity d equation

e expression f formula

g equation h expression

i formula j identity

k equation l formulam identity n equation

o expression

2 a eg. 3p 5 b eg. 3p p 2p

c eg. 3p 5 d eg. q 3p 5

Exercise 28E

1 x 1

5

y

2 x y

5

6

3 h 2x(x

b

3)

4 m W

5

3

a

a

5 c 5

b

a

3

6 q 2p

r

3

4r

7 a R

b cm

8 x 7

5

y

2

1

y

5

9 w y

3

2

10 x 1

1

y

y

11 x

1

a

ab

12 A

5

p2

13 a l 4

T

2g2,

b g 4

T

2

2l

10

x

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ANSWERS

Chapter 29

Exercise 29A

1 a 13 cm, b 41 cm, c 10 cm

2 a 7 cm, b 35 cm, c 15 cm

3 a 10.8 cm, b 10.3 cm, c 10.4 cm, d 11.6 cm

4 a 9.56 cm, b 7.88 cm, c 12.3 cm, d 8.03 cm5 a 12.6 cm b 15.2 cm c 14.4 cm

d 5.77 cm e 20.8 cmf i ii 6.42 cm

Exercise 29B

1 3.47 m 2 10.8 cm 3 23.3 km 4 52.4 cm2 5 28.2 cm

6 a 3.20 m,b i 4.33 m, ii 2.33 m,c 8.66 m

7 a 15 cm, b 36 cm

8 2.85 cm

9 a i 289 ii 289b equalc triangle is right-angled

10 Triangles 1, 2, 4 and 6 are right-angled

Exercise 29C

1 a 10 b 26 c 212 14.6d 424 20.6 e 29 f 117 10.8

2 a i 5 ii 50 7.07 iii 5b 52 52 50 so triangle is isosceles and right-angled at A.

3 a PQ 10 3.16, QR 160 12.6,PR 170 13.0

b 10 160 170 so triangle is right-angled.c 20

4 a (10, 21)b i 34 ii 17

5 a 13b B, C, E lie on the circle

6 a (2.5, 0.5) b 20.2

7 a i 25 ii 25 iii 25 iv 25

b ABCD is a rhombus

8

AB2 (p a)2 (q b)2

AB (p a)2 (q b)2

Exercise 29D

1 a 0.3420 b 0.9511 c 0.5d 14.3007 e 1 f 0.9461g 0.0699 h 0.2538 i 0.2538

2 a 5.47 cm b 17.1 cm c 11.6 cmd 7.79 cm e 25.5 cm f 9.18 cmg 26.4 cm h 10.4 cm i 11.3 cm

3 a 18.1 cm b 13.4 m c 10.8 cm

4 a i 9.96 cm ii 8.36 cmb 5.30 cm c 13.7 cm d 68 cm2

5 a 24.2 cm b 29.6 cm

Exercise 29E

1 a 60 b 25.5 c 53.1d 43.8 e 58.4 f 63.8g 2.7 h 15.9

2 a 37.7 b 46.2 c 19.7d 45.6 e 47.1 f 43.6

3 a 36.3 b 38.9 c 32.3

4 a 41.0 b 57.5 c 98

Exercise 29F

1 a 7.89 cm b 26.3

2 a 1.4 m b 73.7

3 a i 1.45 m ii 5.44 m iii 2.54 m

4 a 16.8 m b 64.5

5 a 46.9 m b 88.3 m

6 a 2.87 cm b 16.5

7 a i 13.0 km ii 10.9 kmb

i 7.73 km ii 23.8 kmc i 20.7 km ii 34.7 kmd 40.4 km at 059.2

8 a

angle HRP 90

b 50 kmc 076.9

9 32 cm2

10 a 3.84 cmb 16.8 cmc 43 cm2

40P

H

R

40km30km

130

N

N

B (p, q)

pa

qb

A

(a, b)

D E

F

7.8cm10.1cm

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ANSWERS

Chapter 30

Exercise 30A

1 a 3 : 1 b 2 : 3 c 3 : 4 d 3 : 2e 3 : 1 f 5 : 7 g 7 : 8 h 1 : 5

2 a 3 : 10 b 4 : 1 c 2 : 5 d 3 : 10e 5 : 2 f 8 : 7 g 5 : 8 h 7 : 1

3 a 1 : 4 b 5 : 3 c 2 : 5 d 3 : 10e 16 : 25 f 5 : 6 g 5 : 6 : 75 h 2 : 10 : 25

4 a 3 : 2 b 2 : 1 c 3 : 2 d 8 : 3e 16 : 15 f 2 : 9 g 4 : 3 : 6 h 3 : 4 : 6

In questions 5 and 9, n may be written as a decimal.

5 a 1 : 3 b 1 : 4 c 1 : 312 d 1 : 12

e 1 : 130 f 1 :

35 g 1 : 8 h 1 : 1

85

6 1 : 50

7 a 1 : 10 b 10 : 1

8 a 1 : 6

9 a 49 b 4 : 5 c 1 : 1

14

10 1 : 375

Exercise 30B

1 a 6 b 18 c 45

2 a 20 g b 60 g c 0.5 kg or 500 g

3 a 10 kg b 15 kg

4 a 4 cm b 6.5 cm c 1.3 cm

5 a 30 km b 21 km c 37.5 km

6 1.5 m

7 a 7 cm b 20 cm

8 180 000 cm 1.8 km

9 1125 10 1.19 m 11 375 ml12 a 5.8 m b 5.5 cm

13 83.5 km 14 750 15 4

Exercise 30C

1 a 10 : 30 b 6 : 9 c 50 : 10 d 60 : 40

2 7

3 12

4 20

5 Sally 54, Alex 66

6 Plain 6, white 12, milk 18

7 16, 24, 40

8 150 g sugar, 300 g fat, 450 g flour

9 1.20 : 1.80 : 3

10 23.70

11 36.50

12 13.30

Exercise 30D

1 a 2 hours b 5 hours

2 1.60

3 64.05

4 32

5 1.68

6 20 cm

7 a 160 g b 150 g

8 5 onions, 500 g sweet potato, 1000 g (1 kg) chickpeas,212 teaspoons curry powder

9 33.75

10 5.85

11 2.70

12 0.7 m or 70 cm

13 450 g

14 2 hours 20 minutes

15 a $360 b 150

16 832.50

17 80

18 America, by 13.57 or $23.75

Exercise 30E

1 a 10 days b 2 days

2 9 hours

3 10 days

4 4 hours

5 9 hours

6 12 hours

7 9 days

8 34 hour or 45 minutes

9 192 cm

10 40 boxes

11 12 extra bowls

12 8 more pages