hexagon STUVWZ is rotated 180 degrees clockwise about the origin to create hexagon S'T'U'V'W'Z

Answer 1

If hexagon STUVWZ is rotated 180 degrees clockwise about the origin, the resulting hexagon S'T'U'V'W'Z can be obtained by reflecting each vertex of the original hexagon across the x-axis.

Here is the process to obtain the coordinates of each vertex of S'T'U'V'W'Z:

1. Let's assume the coordinates of hexagon STUVWZ are:
S (x_s, y_s)
T (x_t, y_t)
U (x_u, y_u)
V (x_v, y_v)
W (x_w, y_w)
Z (x_z, y_z)

2. Reflect each vertex of the original hexagon across the x-axis. The x-coordinate of each vertex remains the same, while the y-coordinate changes sign. The coordinates of S'T'U'V'W'Z would be:
S' (x_s, -y_s)
T' (x_t, -y_t)
U' (x_u, -y_u)
V' (x_v, -y_v)
W' (x_w, -y_w)
Z' (x_z, -y_z)

The resulting coordinates of hexagon S'T'U'V'W'Z represent the hexagon obtained when hexagon STUVWZ is rotated 180 degrees clockwise about the origin.