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12.3 Transforming shapes

) Exercise 12.3

1 The diagram shows shape A on a coordinate grid. y
Make two copies of the diagram. 4
3
On different copies of the diagram, draw the image of A
A after each of these combinations of transformations. 2
 1  1
a Reflection in the y-axis followed by the translation   0 x
−  2 –4 –3 –2 –1 –1 1 B 2 3 4

b Rotation of 90° anticlockwise, centre (−1, 2) followed –2
by a reflection in the line x = 1

2 The diagram shows triangle B on a coordinate grid. 6 y
Make four copies of the diagram.
5
On different copies of the diagram, draw the image of 4
B after each combination of transformations.
3
5   2
a Translation   , followed by a reflection in the x-axis
1   1

b Rotation of 180°, centre (−3, −2) followed by a –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 x
reflection in the y-axis –1
–2
−  1  –3
c Translation   , followed by a rotation of B
 5  –4
90° clockwise, centre (−2, 1) –5
–6
d Reflection in the line y = −1, followed by a rotation 90°
anticlockwise, centre (2, 2).
y
3 The diagram shows shapes G, H, I, J and K on a coordinate grid.
4
Describe the reflection that transforms: 3
a shape G to shape H G 2 H
b shape G to shape K 1
c shape H to shape J
0 I x
d shape J to shape I. –4 –3 –2 –1 –1 1 2 3 4
J
–2
K
–3
–4

y
4 The diagram shows shapes L, M, N, P and Q on a coordinate grid. 4 L
Describe the translation that transforms: M 3
a shape N to shape L b shape N to shape P N 2
c shape N to shape Q d shape N to shape M 1
e shape L to shape P f shape P to shape M. 0 x
–4 –3 –2 –1 –1 1 P 2 3 4
Q
–2

12 Tessellations, transformations and loci 117