Now, let us look at the following numbers: 11, 1001. Do these have (a) rotational symmetry, (b) reflection symmetry or (c) both symmetries?
Number 11: Has reflection symmetry (vertical line of symmetry between the two digits). Does not have rotational symmetry. ∴ Number 11 has (b) reflection symmetry.
Number 1001: Has reflection symmetry (vertical line through the centre). Has rotational symmetry (looks the same after 180° rotation). ∴ Number 1001 has (c) both symmetries.
Explanation
The chapter extends the concept of symmetry from single digits to multi-digit numbers. Number 11, when written with two identical 1s, has a vertical line of symmetry between the two digits. Number 1001 has both reflection symmetry (vertical line through the centre) and rotational symmetry (when rotated 180 degrees, it reads the same).
Solution Steps
Analyze Number 11 for symmetry: has vertical line of symmetry between the two identical digits.
Check Number 11 for rotational symmetry: does not look the same after rotation.
Analyze Number 1001 for symmetry: has vertical line of symmetry through the centre.
Check Number 1001 for rotational symmetry: looks the same after 180° rotation (1/2 turn).
Conclude: Number 11 has reflection symmetry only; Number 1001 has both symmetries.