Question

(a) In a square, red balls are arranged along one diagonal and yellow balls are arranged along another diagonal. Find the rotational symmetry of the given arrangement?

(b) If ‘X’ is the order of rotation of a regular polygon with ‘n’ sides and ‘Y’ is the number of angles of rotation, what is the value of (X – Y – 1)? [4 MARKS]

Answer 1

(a) Diagram: 1 Mark
Reason: 1 Mark
(b) Solution: 2 Marks

(a) The answer is 2. The given diagram when rotated by 180${}^o$ and 360${}^o$ gives the same figure.


Due to different colours of the two diagonals, the figure won't look the same if it's rotated by 90${}^o$ or 270${}^o$. Hence, it will have a rotational symmetry of only 2.


(b) Order of rotation of a regular polygon with ‘n’ sides = X = n

For e.g. an equilateral triangle and a square repeat the initial position 3 and 4 times respectively for ${360}^{\circ }$ rotation.

Angles of rotation of a regular polygon with ‘n’ sides = Y = n – 1

This is because the last rotation, i.e. ${360}^{\circ }$ is not counted as angle of rotation.

So, X – Y – 1 = n – (n – 1) – 1 = n – n + 1 – 1 = 0