Definition of Order of Rotational Symmetry:
The number of times a figure fits into itself in one complete rotation is called the order of rotational symmetry.
If A° is the smallest angle by which a figure is rotated so that rotated from fits onto the original form, then the order of rotational symmetry is given by \(\frac{360°}{A°}\), [A° < 180°]
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°.
Examples of Order of Rotational Symmetry:
Rectangle (clockwise)
We observe that while rotating the figure through 360°, it attains
original from two times i.e., it looks exactly the same at two positions. Thus,
we say that the rectangle has a rotational symmetry of order 2.
Equilateral triangle (clockwise):
We observe that at all 3 positions, the triangle looks exactly the same when rotated about its center by 120°.
Letter B (clockwise):
We observe that only at one position the letter looks exactly the same after taking one complete rotation.
Windmill (anticlockwise):
We observe that if we rotate it by one – quarter, at 4 positions, it looks exactly the same. Therefore, the order of rotational symmetry is 4.
Solved Examples on Order of Rotational Symmetry:
1. Find the order of rotational symmetry of the following shapes about the point marked.
Solution:
(i)
Order of rotational symmetry = \(\frac{360}{180}\) = 2
(ii)
Order of rotational symmetry = \(\frac{360}{60}\) = 6
2. The figure obtained by giving 2 anticlockwise right-angle turns to letter G is:
Answer: (ii)
● Related Concepts
● 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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