Question

The diagram shows the outline of a 50 cent coin from Fiji. What is its order of rotational symmetry?

(a) 8
(b) 9
(c) 12
(d) 15

Answer 1

Hint: To solve the given question, we will first find out what symmetry is and what rotational symmetry is. Thus, to find the order, we will start rotating the coin about the center and will note how many times while rotating the coin, the figure has looked the same. This will be equal to the order of the rotational symmetry.

Complete step by step solution:
Before we solve the given question, we will first find out what symmetry is and what rotational symmetry is. When an image or a figure looks identical to the original image after the shape is being turned or flipped, then it is called symmetry. Rotational symmetry is the property a shape has when it looks the same after rotation by a particular turn. We have to find the order of rotational symmetry of the coin. The order of rotational symmetry is the number of times it can be rotated around a full circle and still looks the same. Let us assume that the angle of rotation is \[\theta .\] Initially, \[\theta =0.\] Now, we will increase \[\theta \] gradually in the clockwise direction. We will notice that when \[\theta \] reaches \[{{30}^{\circ }}\] the figure looks exactly the same as the figure at \[{{0}^{\circ }}.\] Thus, at \[\theta ={{60}^{\circ }},\] the figure is rotationally symmetric. Now, we will again increase the angle. At, \[\theta ={{60}^{\circ }},\] the figure will be again rotationally symmetric. Similarly, the other angles at which the figure will be rotationally are \[{{90}^{\circ }},{{120}^{\circ }},{{150}^{\circ }},{{180}^{\circ }},{{240}^{\circ }},{{270}^{\circ }},{{300}^{\circ }},{{330}^{\circ }},{{360}^{\circ }}.\] Thus, there are total of 12 angles at which the figure is rotationally symmetric. Hence, its order is 12.
Therefore, option (c) is the right answer.

Note: The question can also be solved in an alternate way as shown. The figure is a regular dodecagon i.e. a polygon having 12 sides, Now, the order of symmetry of an n – sided polygon is n provided all its sides have the same length. In our case, there are 12 sides, so the order will be 12.