Question

what is the final transformation in this sequence of transformations mapping pre - image vwxyz to final image vwxyz? 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 moves a figure without rotation or reflection. The orientation of the figure in V'W'X'Y'Z' and V"W"X"Y"Z" is different, so it's not a translation up and to the right.

Step2: Analyze reflection

A reflection across a point would not result in the orientation change seen here. Reflection across a point would not map the figure in the way shown.

Step3: Analyze rotation about V'

If we consider a 90 - degree rotation about V', the figure would not be in the position of V"W"X"Y"Z" as the relative positions of the vertices would be incorrect.

Step4: Analyze rotation about Z'

If we rotate the figure V'W'X'Y'Z' 180 degrees about Z', the vertices will be mapped to the positions of V"W"X"Y"Z" correctly.

Answer:

a rotation 180° about Z'