### 2D Rotational Symmetry Practice

#### Question 1

Which of the following figures have 2D rotational symmetry with their order of symmetry correctly labeled?

• I

Order 1

• II

Order 2

• III

Order 3

• IV

Order 4

A. I & II
B. II & III
C. III & IV
D. I & IV

### Step by Step Solution

• #### Step 1

When we rotate this shape for 360°, we will realize that it only fits onto itself once.

Hence, this shape has order of symmetry of 1 but has no rotational symmetry.

• #### Step 2

When we rotate this shape for 360°, we will see that it fits onto itself twice.

Therefore, this shape has rotational symmetry and rotational symmetry of order 2.

• #### Step 3

When we rotate this shape for 360°, we will see that fits onto itself 6 times.

Therefore, this shape has rotational symmetry and rotational symmetry of order 6.

• #### Step 4

The flower's petals are different in shapes. Therefore, it can only fits onto itself after one full turn.

Hence, this shape has symmetry of order 1 but has no rotational symmetry.

• #### Step 5

From the steps above, only figures II and III has rotational symmetry with correctly labeled order of symmetry. Hence, the answer is B.