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
From Definition of Order of Rotational Symmetry to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.