\( \begin{aligned}
&\text{Compare coordinates of matching vertices. If }(a,b)\to(b,a),\text{ it's a reflection in }y=x.\\
&\text{Also check that both shapes are the same size (congruent).}
\end{aligned} \)
Question 21:
[Ad Space]
\[ \begin{array}{l}
\text{Describe fully the single transformation that maps triangle A onto triangle B.}
\end{array} \]
Answer:\( Reflection in the line $y=x$. \)
Explanation:
\begin{aligned}
&\text{Triangles A and B are congruent, so the transformation is isometric.}\\
&\text{Their orientation is reversed, so it is not a translation or rotation of }180^{\circ}.\\
&\text{Checking corresponding vertices shows }(a,b)\mapsto(b,a),\text{ so each point is mirrored across }y=x.\\
&\therefore\;\text{the single transformation is a reflection in the line }y=x.
\end{aligned}