Question

what is the final transformation in the composition of transformations that maps preimage cdef to image cdef? options: a 180° rotation about point g, a 90° rotation about point g, a translation to the right, a reflection across line m

Explanation:

To determine the transformation from \( CDEF \) to \( CDE'F' \), we analyze the options:

Step 1: Analyze Rotation (Option B: \( 90^\circ \) rotation about \( G \))

A \( 90^\circ \) rotation about a point (here, \( G \)) would reorient the shape by \( 90^\circ \) (clockwise or counterclockwise) around \( G \). The diagram suggests the shape \( CDEF \) is rotated around \( G \) to form \( CDE'F' \), matching a \( 90^\circ \) rotational transformation.

Step 2: Eliminate Other Options

• Option A (\( 180^\circ \) rotation about \( G \)): A \( 180^\circ \) rotation would flip the shape symmetrically through \( G \), which does not match the orientation change here.
• Option C (Translation right): Translation moves the shape without rotation, but the orientation of \( CDEF \) changes (e.g., sides are reoriented), so this is not a translation.
• Option D (Reflection over line \( m \)): Reflection would create a mirror image, but the diagram shows a rotational reorientation, not a mirror flip.

Answer:

B. a \( 90^\circ \) rotation about point \( G \)