Cambridge International Mathematics

404 Transformation geometry (Chapter 20)

EXERCISE 20A

1 Find the image point when:

a (2,¡1) is translated through

¡ 3

4

¢

b (5,2) is translated through

¡¡ 1

4

¢

:

2 If (3,¡2) is translated to (3,1), what is the translation vector?

3 What point has image (¡ 3 ,2) under the translation

¡¡ 3

1

¢

?

4 Find the translation vector which maps:

a A onto E b E onto A

c A onto C d C onto A

e B onto E f D onto E

g E onto C h E onto D

i D onto B j A onto D.

When we

translate point A,

we often label its

image A^0.

5 Triangle ABC has vertices A(¡ 1 ,3),B(4,1) and C(0,¡2):

a Draw triangle ABC on a set of axes.

b Translate the figure by the translation vector

¡ 4

¡ 2

¢

.

c State the coordinates of the image vertices A^0 ,B^0 and C^0.

d Through what distance has each point moved?

6 What single transformation is equivalent to a translation of

¡ 2

1

¢

followed by a

translation of

¡ 3

4

¢

?

7 Find the equation of the image line when:

a y=2x+3is translated

¡¡ 1

2

¢

b y=^13 x+2is translated

¡ 3

0

¢

c y=¡x+2is translated

¡ 2

3

¢

d y=¡^12 x is translated

¡¡ 2

¡ 5

¢

:

When P(x,y) moves under arotationabout O through an

angle ofμto a new position P^0 (x^0 ,y^0 ), then OP=OP^0 and

POPb^0 =μwherepositiveμis measuredanticlockwise.

O is the only point which does not move under the rotation.

We will concentrate on rotations of 90 o(both clockwise and

anticlockwise) and 180 o.

B ROTATIONS [5.4, 5.6]

A

B

E

C

D

y

x

q P(!'\\@)

P' ' '(! '\\@ )

O

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y:\HAESE\IGCSE01\IG01_20\404IGCSE01_20.CDR Friday, 3 October 2008 3:38:47 PM PETER