Question

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

Explanation:

Step1: Analyze rotation properties

A $180^{\circ}$ rotation about a point flips a figure across that point. Observing the orientation of the pre - image and final image with respect to $Z'$, a $180^{\circ}$ rotation about $Z'$ can map the intermediate image to the final image. A reflection across a point is not a standard transformation term (usually we have reflection across a line). A $90^{\circ}$ rotation about $V'$ would change the orientation in a different way than what is shown. A translation up and to the right would not change the orientation of the figure as seen in the transformation from the intermediate to the final image.

Answer:

a rotation $180^{\circ}$ about $Z'$