Question 12

Rotational symmetry means a figure looks the same after turning it around a central point.

Step 1 — First figure (circle with cross)

This refers to the cross shape. Look at the bottom-middle figure. It has four equal arms. We turn it by 90 degrees. It looks exactly the same. We turn it by 180 degrees. It looks exactly the same. We turn it by 270 degrees. It looks exactly the same. We turn it by 360 degrees. It looks exactly the same. It looks the same 4 times. So, its order of rotational symmetry is 4.

$\boxed{4}$

Step 2 — Second figure (triangle)

This refers to the three-armed figure. Look at the bottom-left figure. It has three arms. We turn it by 120 degrees. It looks exactly the same. We turn it by 240 degrees. It looks exactly the same. We turn it by 360 degrees. It looks exactly the same. It looks the same 3 times. So, its order of rotational symmetry is 3.

$\boxed{3}$

Step 3 — Third figure (circle with three spokes)

This refers to the three-armed figure. Look at the bottom-left figure again. It has three spokes. We turn it by 120 degrees. It looks exactly the same. We turn it by 240 degrees. It looks exactly the same. We turn it by 360 degrees. It looks exactly the same. It looks the same 3 times. So, its order of rotational symmetry is 3.

$\boxed{3}$

<DIAGRAM: Bottom-left figure, a triskelion-like shape made of three bent arms, joined at a central point, each arm ending in a fist.>

Step 4 — Fourth figure (four-blade fan)

This refers to the cross shape. Look at the bottom-middle figure again. It has four blades. We turn it by 90 degrees. It looks exactly the same. We turn it by 180 degrees. It looks exactly the same. We turn it by 270 degrees. It looks exactly the same. We turn it by 360 degrees. It looks exactly the same. It looks the same 4 times. So, its order of rotational symmetry is 4.

$\boxed{4}$

<DIAGRAM: Bottom-middle figure, a cross shape made of four rectangles joined at a central point, with a dot in the center.>

Step 5 — Fifth figure (cross)

This refers to the cross shape. Look at the bottom-middle figure again. It is a cross shape. We turn it by 90 degrees. It looks exactly the same. We turn it by 180 degrees. It looks exactly the same. We turn it by 270 degrees. It looks exactly the same. We turn it by 360 degrees. It looks exactly the same. It looks the same 4 times. So, its order of rotational symmetry is 4.

$\boxed{4}$

<DIAGRAM: Bottom-middle figure, a cross shape made of four rectangles joined at a central point, with a dot in the center.>

Answer

(i) Order of rotational symmetry is 4. (ii) Order of rotational symmetry is 3. (iii) Order of rotational symmetry is 3. (iv) Order of rotational symmetry is 4. (v) Order of rotational symmetry is 4.