Question

What is the order of rotational symmetry and angle of rotational symmetry for this design?

A. $4;{{90}^{\circ }}$
B. $6;{{120}^{\circ }}$
C. $8;{{60}^{\circ }}$
D. $8;{{45}^{\circ }}$

Answer 1

Hint: We should remember that the angle of rotational symmetry is the smallest angle for which the figure can be rotated to coincide with itself. The order of symmetry is the number of times the figure coincides with itself as it rotates through ${{360}^{\circ }}$. We can keep this concept in mind and find the answer for the given figure.

Complete step by step answer:
Let us rotate the given shape and see at which angle the shape remains the same. We find that after rotating the shape, that it remains the same at ${{90}^{\circ }}$ .

So, we can conclude that the angle of rotational symmetry of the given shape is ${{90}^{\circ }}$as we know that it is the smallest angle for which the shape will coincide with itself when rotated. Now, let us rotate the shape through ${{360}^{\circ }}$ and see how many times it coincides with itself as that would be the order of symmetry for the shape. After rotating through ${{360}^{\circ }}$ , we find that the shape coincides with itself 4 times. Therefore, the order of symmetry would be 4.
Therefore, we can say that the angle of rotational symmetry for the given shape is ${{90}^{\circ }}$ and the order of rotational symmetry will be 4.

So, the correct answer is “Option A”.

Note: We must remember that many geometrical shapes appear to be symmetrical when they are rotated through ${{180}^{\circ }}$ or when they have the same angle, clockwise or anti-clockwise. For example, square, circle, hexagon, etc. A scalene triangle does not have symmetry if rotated, since the shape is asymmetrical. If a shape only coincides with itself once after one full rotation, then there is no symmetry at all.