Question

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

Explanation:

Step1: Analyze translation

Translation up and to the right would just shift the figure without changing orientation. But the orientation of the final - image has changed, so this is incorrect.

Step2: Analyze reflection across point \(Z'\)

Reflection across a point is not a common transformation type in the standard sense. Also, the figure's orientation and position do not match what a reflection across a single point would produce.

Step3: Analyze rotation 90° about \(V'\)

If we rotate 90° about \(V'\), the figure's orientation and position do not match the final - image.

Step4: Analyze rotation 180° about \(Z'\)

When we rotate a figure 180° about a point, the orientation of the figure changes in a way that matches the transformation from \(V'W'X'Y'Z'\) to \(V''W''X''Y''Z''\). The relative positions of the vertices with respect to the center of rotation \(Z'\) are consistent with a 180 - degree rotation.

Answer:

a rotation 180° about \(Z'\)