Question

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

Explanation:

Step1: Analyze each option

• Translation: Changes position but not orientation.
• Reflection across a point: Not a standard transformation.
• Rotation about \(V'\): Doesn't match the final - image's relation.
• Rotation \(180^{\circ}\) about \(Z'\): When a figure is rotated \(180^{\circ}\) about a point \(P\), each point \(Q\) of the pre - image has an image \(Q''\) such that \(P\) is the mid - point of the segment \(QQ''\). Looking at the pre - image \(V'W'X'Y'Z'\) and the final image \(V''W''X''Y''Z''\), \(Z'\) is the common vertex. If we consider the rotation of each point of \(V'W'X'Y'Z'\) about \(Z'\) by \(180^{\circ}\), we can get \(V''W''X''Y''Z''\).

Answer:

a rotation \(180^{\circ}\) about \(Z'\)