South African Mathematics Olympiad

Answer E. If we reflect $P(-1;-1)$ in the $x$-axis to map to $Q(-1;1)$ we obtain 3 squares with the $x$-axis as a line of symmetry, as shown in the diagram. Two of the cases have $PQ$ as an edge/side and in one case $PQ$ is a diagonal of the square. Similarly, if we reflect $P$ in the $y$-axis to $R$, then there are three possible squares. However, one of these is the same as before, so in total there are exactly five squares possible.