Cambridge International Mathematics

O

y

x

O

y

123 6 x

ABA' B'

DCD' C'

1

3

420 Transformation geometry (Chapter 20)

8 Suppose R is a clockwise rotation of 90 oabout O(0,0)and M

is a reflection in the line y=¡x.

Use a triangle on a set of axes like the one given to find the

single transformation equivalent to:

a RM b MR.

Review set 20B

#endboxedheading

1 Find the image of(3,¡2)under a reflection in:

a thex-axis b the line y=¡x c the line y=4.

2 Find the image of(3,¡7)under:

a a translation of

¡ 2

¡ 4

¢

followed by a reflection in they-axis

b a reflection in thex-axis followed by a reflection in the line y=¡x.

3 Find the image of:

a (3,5) under an enlargement with centre O(0,0)and scale factor 3

b (¡ 2 ,3) under a stretch with invarianty-axis and scale factor 2

c (¡ 5 ,¡3) under a stretch with invariantx-axis and scale factor^12.

4 Find the equation of the image of y=¡ 2 x+1under:

a a translation of

¡ 3

¡ 1

¢

b a reflection in the line y=x

c a 90 oanticlockwise rotation about O(0,0)

d a stretch with invariantx-axis and scale factor^12.

5 The object ABCD is mapped onto A^0 B^0 C^0 D^0.

Describe the transformation fully.

6 Consider f(x)=^12 x+3. On separate axes, graph:

a y=f(x) and y=f(x+1) b y=f(x) and y=f(x)+1

c y=f(x) and y=¡f(x) d y=f(x) and y=^12 f(x)

7 y=f(x) is mapped onto y=g(x) by a single

transformation.

a Describe the transformation fully.

b Writeg(x)in terms off(x).

8 Find theinversetransformation of:

a a reflection in thex-axis b a 180 orotation about O(0,0)

c an enlargement about O(0,0)with scale factor k=3.

9 M is a reflection in they-axis and R is an anticlockwise rotation through 90 oabout the origin

O(0,0). Find the single transformation which is equivalent to: a MR b RM.

y

O x

2

1

yx¡=¡¦()

ygx¡=¡()

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_20\420IGCSE01_20.CDR Thursday, 23 October 2008 2:48:13 PM PETER