Rotational symmetry | Symmetry | Assessment | English | Grade 7

Rotation turns an object about a fixed point. This point is called _________.

• Angle of rotation

• Order of rotation

• Centre of rotation

• Line of symmetry

Answer explanation

Rotation turns an object about a fixed point. This point is called centre of rotation. Hence option 3 is the right answer.

Order of rotational symmetry of a scalene triangle is _______.

• 3

• 2

• 1

• 0

Answer explanation

A scalene triangle has a rotational symmetry of order 1. Hence, option 3 is the right answer.

Which of the following letters has a rotational symmetry of order more than 1?

• M

• A

• T

• H

Answer explanation

The order of rotation of letter M, A and T is 1. The order of rotation of letter H is 2. Hence option 4 is the right answer.

The order of rotational symmetry for the adjoining figure is ______.

• Infinite

• 6

• 3

• 1

Answer explanation

In a complete turn of 360⁰, the number of times the figure coincides with the original position is called its order of rotation. In the given figure, let us mark a point and rotate the figure by an angle of 60⁰, 120⁰, 180⁰, 240⁰, 300⁰ and 360⁰. We will find that in each case we will get the figure in the exact state as the original figure. Therefore in given figure the order of rotation is 6. Hence option 2 is the right answer.

Which of the following options has a rotational symmetry of order 2?

• 
• 
• 
• 

Answer explanation

When a rectangle is rotated by 180⁰ and 360⁰, then the original rectangle is obtained. Hence the order of rotation of the rectangle is 2. Hence option 1 is the right answer.

Which of the following statements is true? (i) The order of rotational symmetry of a circle is 360. (ii) The order of rotational symmetry of a semicircle 1.

• Only statement (i)

• Only statement (ii)

• Both statement (i) and statement (ii)

• Neither statement (i) nor statement (ii)

Answer explanation

When a circle is rotated by any angle, then in each case the circle occupies the same position as the original position. We know that between 0 and 1 there are infinite rational numbers. Since a circle can be rotated by an angle which is less that 1⁰, therefore the order of rotation of a circle is infinite. Hence the statement (i) is false. When a semicircle is rotated by different angles, it occupies the same position as the original position only after a rotation of 360⁰. Therefore the order of rotation of semicircle is 1. Hence statement (ii) is true. So option 2 is the right answer.

State whether the following sentence is true or false. After rotating a figure by 120° about its centre, the figure coincides with its original position. This will happen again if the figure is rotated at an angle of 240°.

• TRUE

• FALSE

Answer explanation

If after rotating a figure by 120° about its centre, the figure coincides with its original position, it means that the order of its rotational symmetry is 3. Therefore, the figure will coincide with original shape at 120°, 240° and 360°. So option 1 is the correct answer.