Question 8.5.8: Rotational Symmetries Determine whether the polygon shown in......
Rotational Symmetries
Determine whether the polygon shown in Fig. 8.76 has rotational symmetry about point P for rotations through each of the following angles.
a) 90° b) 180°
a) To determine whether the polygon has 90° counterclockwise rotational symmetry about point P, we rotate the polygon 90° as shown in Fig. 8.77(a). Compare Fig. 8.77(a) with Fig. 8.76. Notice that the position of the polygon after the rotation in Fig. 8.77(a) is different than the original position of the polygon (Fig. 8.76). Therefore, the polygon does not have 90° rotational symmetry about point P.
b) To determine whether the polygon has 180° counterclockwise rotational symmetry about the point P, we rotate the polygon 180° as shown in Fig. 8.77(b) on page 491. Compare Fig. 8.77(b) with Fig. 8.76. Notice that other than vertex labels, the position of the polygon after the rotation in Fig. 8.77(b) is identical to the position of the polygon before the rotation (Fig. 8.76). Therefore, the polygon has 180° rotational symmetry about point P.
