Questions: Octagon PQRSTVWZ is a regular octagon with its center at point C. Which transformations will map octagon PQRSTVWZ onto itself? Select each correct transformation Select ALL that apply. reflecting over segment RW rotating 135 degrees around point C reflecting over segment OV rotating 45 degrees around point C

Octagon PQRSTVWZ is a regular octagon with its center at point C.

Which transformations will map octagon PQRSTVWZ onto itself? Select each correct transformation Select ALL that apply. reflecting over segment RW rotating 135 degrees around point C reflecting over segment OV rotating 45 degrees around point C

Transcript text: Octagon PQRSTVWZ is a regular octagon with its center at point $C$. Which transformations will map octagon PQRSTVWZ onto itself? Select each correct transformation Select ALL that apply. reflecting over segment RW rotating 135 degrees around point $C$ reflecting over segment $O V$ rotating 45 degrees around point $C$

Solution

Solution Steps

Step 1: Identify the Symmetries of the Octagon

An octagon has several symmetries, including rotational and reflectional symmetries. Specifically, a regular octagon can be rotated by multiples of 45 degrees around its center and can be reflected over lines that pass through its center and vertices or midpoints of opposite sides.

Step 2: Analyze Each Transformation

Reflecting over segment RW: This is not a line of symmetry for the octagon.
Rotating 90 degrees around point Z: This does not map the octagon onto itself because the center of rotation should be the center of the octagon, not a vertex.
Rotating 135 degrees around point C: This is a valid rotation for a regular octagon, as 135 degrees is a multiple of 45 degrees.
Reflecting over segment QV: This is a line of symmetry for the octagon.
Reflecting over segment TZ: This is not a line of symmetry for the octagon.
Rotating 45 degrees around point C: This is a valid rotation for a regular octagon, as 45 degrees is a multiple of 45 degrees.
Reflecting over segment SZ: This is not a line of symmetry for the octagon.