Question

The order of symmetry for the given figure is –

A) 6
B) 2
C) 3
D) 4

Answer 1

We need to understand the concepts of symmetry of rotation of an object of any shape to give a number value to this physical quantity. We are given an object shaped cross-like as we can see in the figure for which we have to apply our knowledge.

Complete answer:
We know that the symmetry of rotation of an object is the number of times it can be turned about a fixed point before a full circular rotation is achieved when the symmetry of the object is maintained after each turn. It is an important property which can be employed in various experiments from an engineering point of view. The idea of the rotation symmetry gives one the different possibilities on construction of different structures with minimum resources and expenditure.
Now, let us consider the shape given to us. Let us name each of its ends as A, B, C and D as shown below.

Let us consider rotating this shape in the anti-clockwise direction. We can see that when the shape is rotated to the right angle, the symmetry of the shape is retained as shown below.

We can see this happening each time it is rotated at right angles as –

And finally, after the fourth rotation it has done a full rotation, it comes back to the initial condition, which is no different from the other three cases.

From the above cases, we understand that the rotational symmetry of the given shape is 4.

The correct answer is option D.

Note:
The rotational symmetry of a shape is in all ways related to its shape and the number of sides of the object. The circle is said to have the maximum, infinite, number of rotation symmetries. The regular polygons usually have the rotation symmetry equal to their number of sides.