Page 119 - Cambridge+Checkpoint+Mathematics+Coursebook+9

12.3 Transforming shapes

5 The diagram shows triangles R, S, T, U, V and W on a coordinate grid. y
Describe the rotation that transforms: 4
a triangle R to triangle S R 3
b triangle S to triangle T S 2
c triangle T to triangle U T 1 U
d triangle U to triangle V –4 –3 –2 –1 0 1 2 3 4 x
–1
e triangle V to triangle W. W
–2
–3 V
–4

6 The diagram shows three shapes X, Y and Z y
on a coordinate grid. 6
Make three copies of the grid. 5
On the first grid draw shape X, on the second grid draw Y 4 X
shape Y and on the third grid draw shape Z. 3
a On the first grid draw the image of X after the 2
combination of transformations: 1
i reflection in the line y = 1 followed by a rotation 90° –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 x
anticlockwise, centre (2, −3) –1 Z
ii rotation 90° anticlockwise, centre (2, −3), followed –2
–3
by a reflection in the line y = 1. –4
b On the second grid draw the image of Y after the –5
combination of transformations: –6
i reflection in the line x = −1 followed
 2 
by the translation  
 2  −  5
ii translation   followed by a reflection in the line x = −1.
−  5

c On the third grid draw the image of Z after the combination of transformations:
i a rotation of 180°, centre (0, 0), followed by a reflection in the line y = 2
ii a reflection in the line y = 2 followed by a rotation of 180°, centre (0, 0).
d i What do you notice about your answers to i and ii in parts a, b and c?
ii Does it matter in which order you carry out combined transformations? Explain your answer.
iii Write down two different transformations that you can carry out on shape Z so that the final
image is the same, whatever order you do the transformations.

7 The diagram shows shapes A, B, C, D and E on a
coordinate grid.
a Describe the single transformation that transforms: y
i shape A to shape B 6
ii shape B to shape C 5 B
iii shape C to shape D. 4
b Describe a combined transformation that transforms: A 3
i shape A to shape D 2
ii shape B to shape E. 1 C D
E 0 x
–6 –5 –4 –3 –2 –1 1 2 3 4 5 6
–1

118 12 Tessellations, transformations and loci