We now try those 3 strategies for different starting points marked on the map (1, 2, 3 and 4). If the point A is moved onto one of those 4~positions, the the route for each strategy for getting to B is shown and the distance recorded in the table below.

You will notice that irrespective of the starting position, Ann's route, Bob's route and Corey's route are all the same length for each route from A to B.

\begin{center}
\includegraphics[width=6.5cm]{PISA/2022/PISA_2022_Mathematics_items_Exo6_IMG6.jpg}
\qquad
\includegraphics[width=6.5cm]{PISA/2022/PISA_2022_Mathematics_items_Exo6_IMG7.jpg}

\bigskip

\includegraphics[width=6.5cm]{PISA/2022/PISA_2022_Mathematics_items_Exo6_IMG8.jpg}
\qquad
\includegraphics[width=6.5cm]{PISA/2022/PISA_2022_Mathematics_items_Exo6_IMG9.jpg}

\medskip

\begin{tabular}{|*4{c|}} \hline
\multirow{2}{*}{Position of A} & \multicolumn{3}{c|}{Distance from A to B (in units)} \\ \cline{2-4}
& Ann's route & Bob's route & Corey's route \\ \hline
1 & 7 & 7 & 7 \\ \hline
2 & 5 & 5 & 5 \\ \hline
3 & 4 & 4 & 4 \\ \hline
4 & 3 & 3 & 3 \\ \hline
\end{tabular}
\end{center}

\begin{enumerate}
	\item Explain why all three strategies produce routes that are equal in length.
\end{enumerate}

