Page 166 - Mathematics Coursebook

17.2 Rotating shapes

) Exercise 17.2

1 Copy each diagram and rotate the shape about the centre C by the given number of degrees.
a b c d

C C C C C C C C C C C C
C C C C

180° 180° 180° 180° 90 ° 90° anticlockwiseanticlockwise 90 ° 90° clockwise 180° 180° 180°
180°
°
°
90° clockwiseclockwiseclockwise
90
90° anticlockwiseanticlockwise
90
2 Copy each diagram and rotate the shape about the centre C by the given fraction of a turn.
a b c d
C C C C C C C C C C C C
C C C C

1 / 2 turn 1 / 2 turn / 2 turn 1 / 2 turn 1 / 4 1 / 4 1 / 2 turn 1 / 2 turn / 2 turn 1 / 2 1 turn 1 / 4 1 / 4
1
1
1
1
1
/ 4 turn anticlockwise turn anticlockwise turn anticlockwise turn anticlockwise
/ 4 turn clockwise turn clockwise turn clockwise turn clockwise
/ 4
/ 4
3 Copy each diagram and rotate the shape, using the given information.
a y y y y b y y y y y c y y y y d y y
y
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
x
x
x
x 5 6 4 3
x 5 6 4 3
0 1 2 0 3 1 2 0 4 3 1 2 0 5 6 4 3 1 2 x 5 6 4 x 0 5 6 1 2 0 3 1 2 0 4 3 1 2 0 5 6 4 3 1 2 x 5 6 4 x 0 5 6 1 2 0 3 1 2 0 4 3 1 2 0 5 6 4 3 1 2 x 5 6 4 x 0 5 6 1 2 0 3 1 2 0 4 3 1 2 0 5 6 4 3 1 2 x 5 6 4 x 5 6 x
x 5 6 4 3
x 5 6 4 3
90° anticlockwise 180° 90° clockwise 180°
centre (1, 3) centre (3, 3) centre (1, 1) centre (4, 3)
4 The diagram shows seven triangles. y
8 To describe a rotation you need to:
Describe the rotation that takes: 7 A
B
6 1 give the number of degrees or
a triangle A to triangle B 5 E
C fraction of a turn
b triangle B to triangle C 4
3 D
c triangle C to triangle D 2 2 if the turn is not 180°, say
d triangle C to triangle E 1 G F whether the turn is clockwise
0
e triangle F to triangle G. 0 1 2 3 4 5 6 7 8 x or anticlockwise
3 give the coordinates of the
5 a Copy this diagram.
Follow these instructions to make a pattern. centre of rotation.
i Rotate the pattern a quarter-turn clockwise about the
centre C.
ii Draw the image.
iii Rotate this new image a quarter-turn clockwise about the centre C.
iv Draw the image.
v Rotate the third image a quarter-turn clockwise about the centre C. C
vi Draw the image.
b What is the order of rotational symmetry of the completed pattern?

17 Position and movement 165