Question

polygons efghijk and efghijk are congruent. which single transformation was used on polygon efghijk to create polygon efghijk? a. reflection across \\(\overleftrightarrow{ef}\\) b. rotation 180° about the point e c. rotation 90° clockwise about the point e d. rotation 90° counterclockwise about the point e

Explanation:

Step1: Analyze Reflection (Option A)

A reflection across \( \overleftrightarrow{EF} \) would mirror the polygon over line \( EF \). But the orientation of the polygon (like the direction of the "arrow" and the rectangle) doesn't match a reflection over \( EF \). So A is incorrect.

Step2: Analyze \( 180^\circ \) Rotation (Option B)

A \( 180^\circ \) rotation about point \( E \) means each point \( (x,y) \) relative to \( E \) becomes \( (-x,-y) \) (in a coordinate system with \( E \) as origin). Looking at the polygon, rotating \( EFGHIJK \) \( 180^\circ \) around \( E \) would map \( F \) to \( F' \), \( G \) to \( G' \), etc., matching the position of \( EF'G'H'I'J'K' \).

Step3: Analyze \( 90^\circ \) Rotation (Option C)

A \( 90^\circ \) clockwise rotation about \( E \) would change the orientation (e.g., a rectangle would become vertical/horizontal in a different way) and doesn't match the given image. So C is incorrect.

Step4: Analyze \( 90^\circ \) Counterclockwise Rotation (Option D)

Similarly, a \( 90^\circ \) counterclockwise rotation about \( E \) would also change the orientation in a way that doesn't match the congruent polygon \( EF'G'H'I'J'K' \). So D is incorrect.

Answer:

B. rotation \( 180^\circ \) about the point \( E \)