what is the final transformation in this sequence of transformations mapping pre-image vwxyz to final image…

what is the final transformation in this sequence of transformations mapping pre-image vwxyz to final image vwxyz?\n○ a translation up and to the right\n○ a reflection across point z\n○ a rotation 90° about v\n○ a rotation 180° about z

what is the final transformation in this sequence of transformations mapping pre-image vwxyz to final image vwxyz?\n○ a translation up and to the right\n○ a reflection across point z\n○ a rotation 90° about v\n○ a rotation 180° about z

Answer

Brief Explanations:

  1. First, observe that VWXYZ maps to V'W'X'Y'Z' via a translation (up and right).
  2. Next, analyze the transformation from V'W'X'Y'Z' to V''W''X''Y''Z'':
    • Z' is a shared vertex, so it is the center of transformation.
    • A 180° rotation about a point maps each point to a position directly opposite the center, with the center as the midpoint. For example, V' maps to V'' such that Z' is the midpoint of V'V'', and this holds for all corresponding vertices.
    • This matches the visual relationship between V'W'X'Y'Z' and V''W''X''Y''Z''.
  3. Eliminate other options: translation would not keep Z' fixed; reflection across a point is not a standard transformation term; a 90° rotation would orient the shape differently, not create the mirrored opposite orientation seen here.

Answer:

a rotation 180° about Z'