Question

What is the order of rotational symmetry of the given figure?

(a) 6
(b) 4
(c) 8
(d) None of these

Answer 1

Hint: First of all we will understand the term rotational symmetry and the order of rotational symmetry. Now, to determine the order of rotational symmetry we will see in how many equal parts the complete angle of 360 degrees is getting divided by the petals present.

Complete step by step solution:
Here we have been asked to find the order of rotational symmetry of the figure provided. First let us learn about the terms rotational symmetry and the order of rotational symmetry.
(1) Rotational Symmetry: - It is the property a shape has when it looks the same after some rotation by a partial turn. For example: - an equilateral triangle will look the same after a partial rotation of 120 degrees.
(2) Order of Rotational Symmetry: - The order of rotational symmetry of a shape is the number of times it can be rotated around a full circle and still look the same. For example: - an equilateral triangle can be rotated 3 times around a full circle, each time at the angle of 120 degrees, so its order of rotation will be 3. In general, a regular polygon having n – sides have ‘n’ lines of symmetry and their order of rotational symmetry is ‘n’.
Now let us come to the question. We have to find the order of rotational symmetry of the figure given below.

We can see that there are six identical petals like structure in the above figure and the angle between the two consecutive petals will be the same. So, each petal can be rotated six times before it gets to its initial position. Therefore, the order of the rotational symmetry will be 6.
Hence option (a) is the correct answer.

Note: You must know about the definitions of the terms mentioned in the question otherwise we may assume it as the simple linear symmetry which will make our answer wrong. Remember that sometimes we will be asked the angle of rotational symmetry of a shape. In this case we have to divide \[{{360}^{\circ }}\] with the obtained order of rotational symmetry to get the answer.