Cambridge International Mathematics

This is T 4

followed by

T 2 ,orT 2 T 4.

second transformation

first

transformation

y

O x

B

B'

A

Transformation geometry (Chapter 20) 419

b Copy and complete the table to indicate the

result of combining the first transformation

with the second transformation.

Review set 20A

#endboxedheading

1 Find the image of:

a (2,¡5)under a reflection in i thex-axis ii the line y=x iii the line x=3

b (¡ 1 ,4)under a clockwise rotation of 90 oabout i O(0,0) ii A(2,1)

c (5,¡2)under a translation of

¡¡ 3

4

¢

d (3,¡1)under an enlargement with centre O(0,0)and scale factor 2

e (3,¡1)under a stretch with invariantx-axis and scale factor (^212)
f (3,¡1)under a stretch with invariant linex=2and scale factor^12.
2 Find the image of(6,2)under a 180 orotation about O(0,0)followed by a translation of
¡¡ 2
3
¢
.
3 Find the equation of the image when y=2x¡ 1 is:
a translated
¡ 2
¡ 4
¢
b reflected in thex-axis
c rotated 90 oclockwise about O(0,0) d stretched with invarianty-axis, scale factor of 2.
4 The object OAB is mapped onto OAB^0.
Describe fully the transformation if B is
(3,3)and B^0 is(3,5).
5 Consider f(x)=2x¡ 1. On separate axes, graph:
a y=f(x)andy=f(x¡2) b y=f(x)andy=f(x)¡ 2
c y=f(x)andy=2f(x) d y=f(x)andy=¡f(x):
6 Copy the graph alongside.
Draw on the same axes, the graphs of:
a y=f(x)+3 b y=¡ 2 f(x):
7 Find theinversetransformation of:
a a translation of
¡ 2
¡ 3
¢
b a reflection in the line y=¡x
c a stretch with invarianty-axis and scale factor 2.

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

T 0 T 0 T 2 T 3

T 1 T 3

T 2

T 3

T 4 T 6

T 5

T 6

T 7 T 7

O

y

(^1) x
()2 ¡3,
4
yx¡=¡¦()
IGCSE01
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Y:\HAESE\IGCSE01\IG01_20\419IGCSE01_20.CDR Thursday, 23 October 2008 2:43:35 PM PETER