Question

example 5 determine whether each figure has rotational symmetry. if so, locate the center of symmetry, and state the order and magnitude of symmetry. 13 14

Explanation:

Step1: Analyze figure 13

The figure 13 has rotational symmetry. The center of symmetry is the intersection point of the lines that connect the corresponding vertices of the rotated figure to the original figure. The order of symmetry is 3 because the figure can be rotated 3 times to coincide with itself within a 360 - degree rotation. The magnitude of symmetry is $\frac{360^{\circ}}{3}=120^{\circ}$, which is the angle of rotation for each step to get the figure to coincide with itself.

Step2: Analyze figure 14

The figure 14 does not have rotational symmetry. There is no point around which the figure can be rotated to coincide with itself within a 360 - degree rotation.

Answer:

Figure 13: Has rotational symmetry. Center of symmetry: Intersection of relevant lines. Order: 3. Magnitude: $120^{\circ}$.
Figure 14: Does not have rotational symmetry.