Mathematics
Assertion: Order of rotational symmetry for the given figure is 4.
Reason: A figure is said to possess rotational symmetry if it fits on itself more than once while being rotated through 360°.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- Assertion (A) is true but Reason (R) is false.
- Assertion (A) is false but Reason (R) is true.
Answer
Assertion (A) is false but Reason (R) is true.
Explanation
The given figure consists of two circles touching each other. To look exactly the same, you would need to rotate it by 180° (half-turn) or 360° (full turn). This means the figure fits on itself twice in one full rotation. Therefore, the order of rotational symmetry is 2, not 4.
So, Assertion is false.
The statement given in the reason is correct and is the standard mathematical definition of rotational symmetry.
So, Reason is true.
Hence, option 4 is the correct option.
Related Questions
Which of the following letters of English alphabet has a rotational symmetry?
- C
- K
- N
- T
Fill in the blanks :
(i) A circle has …………… lines of symmetry.
(ii) The letter S does not possess …………… symmetry.
(iii) A semi-circle is symmetrical about the …………… of its diameter.
(iv) The letter H has …………… line(s) of symmetry.
(v) A quadrilateral having 4 lines of symmetry as well as rotational symmetry of order 4 is …………… .
Write true (T) or false (F) :
(i) A kite possesses a linear symmetry but no rotational symmetry.
(ii) The order of rotational symmetry of a regular hexagon is 6.
(iii) A parallelogram does not have any line of symmetry.
(iv) A square has a point symmetry but rhombus does not.
(v) The letter N does not possess a rotational symmetry.
Assertion: The number of lines of symmetry of a regular polygon is equal to its number of vertices.
Reason: A figure that possesses point symmetry always has line symmetry.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
- Assertion (A) is true but Reason (R) is false.
- Assertion (A) is false but Reason (R) is true.