Page 214 - ICSE Math 8

Example 5: Find the order of rotational symmetry and the angles of rotation of the following figures about
point O.
(a) (b)
O
O

Solution: (a) Order of rotational symmetry = 6
360° 60° 60°
Smallest angle of rotation = = 60° 60°
6 60° 60°
∴ Angles of rotation are 60°, 120° (60° + 60°), 60°
180° (60° + 60° + 60°), 240° (60° + 60° + 60° + 60°),
300° (60° + 60° + 60° + 60° + 60°) and 360° (60° + 60° + 60° + 60° + 60° + 60°)
(b) Order of rotational symmetry = 2
360° 180°
Smallest angle of rotation = = 180°
2 O
∴ Angles of rotation are 180° and 360° (180° + 180°). 180°

EXERCISE 19.2

1. Find the reflection of the following points about x-axis.
(a) (3, 4) (b) (–2, –1) (c) (1, –5) (d) (–10, 7)
2. Find the reflection of the following points about y-axis.
(a) (2, 3) (b) (–6, 1) (c) (8, 0) (d) (–5, –7)
3. Find the reflection of the following points about origin.
(a) (1, –3) (b) (4, –8) (c) (–6, 0) (d) (0, –5)
4. Find the image of the points obtained when the following points are rotated about origin through 180°.
(a) (8, –5) (b) (4, 6) (c) (–3, 7) (d) (10, –2)
5. Find the image of the points obtained when the following points are rotated about origin through 90° in
anticlockwise direction.
(a) (1, –3) (b) (–5, –5) (c) (–8, 11) (d) (–12, 9)
6. Find the image of the points obtained when the following points are rotated about the origin through 90°
in clockwise direction.
(a) (6, 15) (b) (–7, –9) (c) (–4, 4) (d) (11, –10)
7. A point A(–4, 6) is reflected about x-axis to point B. Point B is then rotated through 180° about the origin
in clockwise direction to point C. Find the coordinates of points B and C.
8. The smallest angle through which a geometrical figure has to be rotated about a point O to coincide with
its original position is 72°. Find the order of rotational symmetry of the figure.

AT A GLANCE

¾ A geometrical figure or an object is said to be symmetric if its one half is of exactly the same size and
shape as the other half.

¾ In reflection, the corresponding points of an object and its image are respectively at the same distance
from the fixed straight line known as mirror.

¾ Reflection of a point (x, y) about x-axis is (x, –y).

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