Answer: 1 Mark
Diagram: 1 Mark
Reason: 1 Mark

The figure has two lines of symmetry.

The lines joining the midpoints of the two sides will be the only lines of symmetry here.

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.

Answer: 1 Mark
Diagram with lines of symmetry: 2 Marks
(a) Number of line of symmetry in the figure is 1.

(b)  The figure has 4 lines of symmetry.

(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.

(a) Answer : 1 Mark
     Reason: 1 Mark
(b) Solution: 2 Marks
(a) The answer is 0.
When the line joining the midpoints of opposite sides divides the figure into two equal halves, such lines are called lines of symmetry. But the lines should not pass through the alphabets. Here no lines of symmetry are possible as no such line can be constructed which would divide the table without cutting through the alphabets.
(b) 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 an angle of rotation. If it was counted as an angle of rotation, every object would have an angle of rotation.

So, angles of rotation for a square are ${90}^{\circ }$, ${180}^{\circ }$ and ${270}^{\circ }$. It’s only 3, not 4.

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

On overlapping the original diagram on its mirror image, we get
​

(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

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