Rotational Symmetry


 
 
Concept Explanation
 

Rotational Symmetry

Rotational Symmetry:

A figure which after rotation superimposes the original figure, that is it remains symmetrical and overlaps itself after rotation is said to follow rotational symmetry.

Consider a rotating object, say a  wheel of a bicycle or a wind - mill etc. The fixed point about which the object rotates is called the center of rotation.

             

When an object rotates in the direction of motion of hands of a clock, rotation is called clock wise rotation; otherwise it is said to be anti-clockwise rotation.

Angle of rotation: The angle through which an object rotates (turns) about a fixed point is known as the angle of rotation.

                

An object is said to take a full turn, if the angle of rotation is of  360^{0} . A quarter-turn means rotation by 90^{0}  and a three quarter-turn means rotation by 270^{0} as shown below :

Rotational symmetry :  A figure is said to have rotational symmetry if it fits onto itself more than once during a full turn i,e. rotation through 360^{0}.  OR

A shape has rotational symmetry when it can be rotated and it still looks the same.  

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 overlaps the original object. The minimum order of rotational symmetry a shape can have is 1. For example, for an equilateral triangle ABC, when it is rotated about point X, will take the same shape after a rotation of angle 120° as in figure. Thus, order of rotational symmetry =   frac{360^{0}}{120^{0}} = 3  . 

 

 

 

Sample Questions
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Question : 1

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

Right Option : A
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Question : 2

What is the order of rotational symmetry ?

Right Option : A
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Question : 3

The order of rotational symmetry for the given figure is

Right Option : D
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