Question

which rigid transformation would map $\triangle aqr$ to $\triangle akp$?
\bigcirc a rotation about point a
\bigcirc a reflection across the line containing $\overline{ar}$
\bigcirc a reflection across the line containing $\overline{aq}$
\bigcirc a rotation about point r

Explanation:

A rigid transformation preserves size and shape. Observing the diagram, $\overline{AQ} \cong \overline{AP}$, $\overline{AR} \cong \overline{AK}$, and $\angle QAR \cong \angle PAK$. Rotating $\triangle AQR$ around point A will align its corresponding sides and angles with $\triangle AKP$, mapping one triangle to the other. The other options do not match the congruent segment and angle relationships shown.

Answer:

a rotation about point A