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(i) Correct answer: 1 Mark
(ii) Correct answer: 2 Marks
(i) Z, H, N have rotational symmetry.
If the given alphabets are rotated about a line passing through their centres, it resembles the same alphabet.
(ii)
(a)
Original Figure
Rotational figures
Order of rotational symmetry


2
(b)
Original Figure
Rotational figure
Order of rotational symmetry


2

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Figures: 1 Mark each
(i) 1line of symmetry

(ii) 1 line of symmetry​​​​​​​

(iii) 1 line of symmetry

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Completed Figures: 1Mark each
(i)

(ii)

(iii)

(iv)

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Figures with order of symmetry 4: 1 Mark
Figures with order of symmetry 3: 1 Mark
Figures with order of symmetry 2: 1 Mark
Figures with order of symmetry 1: 1 Mark
Figures (a) and (f) will look the same if rotated by 90${}^o$, 180${}^o$, 270${}^o$ or 360${}^o$. Hence, they have an order of 4.
Figures (b) and (e) will look the same if rotated by 120${}^o$, 240${}^o$ or 360${}^o$. Their order of rotational symmetry will thus be 3.
If we rotate figure (d) by 180${}^o$ or 360${}^o$, we will get the same figure. Hence, it has an order of 2.
But option (c) has an order of only 1 since the same figure can be obtained if the figure is rotated by 360${}^o$.

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Answer: 2 Marks
Rotate the given equilateral triangle about its centre to 120 degrees it looks the same.
If you rotate the given equilateral triangle by 120 degrees, 240 degrees,360 degrees it will be the same. Order of rotational symmetry is 3.

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(a) Exact figure: 2 Marks
(b) Correct answer: 2 Marks
(a)

(b)

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(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 ${360}^{∘}$ rotation.
Angles of rotation of a regular polygon with ‘n’ sides = Y = n – 1
This is because the last rotation, i.e. ${360}^{∘}$ is not counted as angle of rotation.
So, X – Y – 1 = n – (n – 1) – 1 = n – n + 1 – 1 = 0

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(a)Calculations: 1 Mark
Result: 1 Mark
(b) Answer: 1 Mark
(c)Answer: 1 Mark
(a) The given polygon will be a rectangle.
Perimeter = 24
2(a+b)= 24
Put a=9 [given]
b = 3
Area of the rectangle = (9)*(3)
= 27 $m^2$
(b)The number of positions in which the object looks exactly the same is called the order of rotational symmetry. The order of symmetry of the given figure is 2.
(c)The number of position in which the object look exactly the same is called the order of rotational symmetry. The order of symmetry of the given figure is 2.

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(a) Exact figure: 2 Marks
(b) Correct answer: 2 Marks
(a)

(b) Line symmetry, mirror symmetry and reflection symmetry are nearly same.

If you fold the figure along the line representing the water level, then the lower half will perfectly align with the upper half. This means the water level is the line of symmetry. This happens because of reflection. The upper and lower halves cannot be different.
At conceptual level, there is no difference between line symmetry and mirror/reflection symmetry

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Mirror image : 1Mark
Final image : 2 Marks
The mirror image of the above diagram will be

On overlapping the original diagram on itsmirror image, we get
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