Page 226 - Start Up Mathematics_7

Order of rotational symmetry
The number of times a figure looks exactly the same as its original shape in a complete turn
(rotation of 360°) is called the order of rotational symmetry.
360°
Thus, order of a rotational symmetry =

Example 6: Can you find the order of rotational symmetry for the letter H?

Solution: The letter H is rotated in the clockwise direction each time by an angle of 180°.
(Note: A ‘•’ is put to make comparison of figures easier. It is not a part of the figure.)

Fig. 1 Fig. 2 Fig. 3
Figure 1 shows the original position of letter H.

Figure 2 shows the position of letter H after a rotation of 180° from its original
position in clockwise direction. It looks like its original shape.
Figure 3 shows the position of letter H after a rotation of 360° from its original

position in clockwise direction. It looks exactly the same as it was in its original
position. (Is it obvious?)

We observe that the letter H looks exactly the same (i.e., H) twice in a complete
revolution of 360°. Hence the order of rotational symmetry is 2.
Example 7: Observe various positions of a square. Fig. 1 is the initial position. Rotation by 90°

about the centre of rotation O leads to Fig. 2. To obtain Fig. 3, Fig. 4 and Fig. 5
successive rotations through 90° are done. In this manner after four quarter-turns,
the point P comes back to its original position (note the position of P).

P P P
90° 90°
O O O O
O
90° 90°
P P
Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5

(a) What is the centre of rotation of the square?
(b) What is the angle of rotation?
(c) Find the direction of rotation.
(d) What is the order of rotational symmetry? Why?
Solution: (a) The centre of rotation is the point of intersection of its diagonals, i.e., O.

(b) The angle of rotation is 90°.
(c) The direction of rotation is clockwise.
(d) The order of rotational symmetry is 4 (i.e., 360° ÷ 90°) which gives the number
of times the square looks exactly the same as its original position in one full
turn.

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