What is rotational symmetry?
When the figure is turned about a fixed point; it is called rotation.
The
shapes and objects that look the same after a certain amount of rotation are
said to have rotational symmetry. Some shapes look the same after half a turn.
If we turn English alphabet S around a centre point by 180° we get the alphabet
S in the same position. The angle of turning during a rotation is called the
angle of rotation. A complete turn means 360°, so a half turn means 180° and a
quarter turn means 90°.
This rotation can be: (a) clockwise (b) anticlockwise
The fixed about which the figure is rotated is called centre of rotation.
The angle of turning during rotation is called the angle of rotation.
A quarter turn means a rotation of 90°
A half turn means a rotation of 180°
A full turn means a rotation of 360°
A figure is said to have rotational symmetry if it onto more than once during a complete rotation, i.e., 360°
Take a square piece and draw lines, as shown in the figure. Place a pin in the centre where the lines meet. Now, rotate this square by 90° about its centre. The square looks exactly the same. In a full turn 360° there are 4 positions when the square looks exactly the same.
Thus, a square has a rotational symmetry of order 4 about its centre of rotation. Hence, the angle of rotation is 90°.
Order of rotational symmetry = \(\frac{360}{\textrm{Angle of Rotation}}\)
A figure has a rotational symmetry of order 1, if it can come to its original position after full rotation or 360°.
● Related Concepts
● Order of Rotational Symmetry
● Reflection of a Point in x-axis
● Reflection of a Point in y-axis
● Reflection of a point in origin
● Rotation
● 90 Degree Clockwise Rotation
● 90 Degree Anticlockwise Rotation
7th Grade Math Problems
8th Grade Math Practice
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