On the scale drawing, P, Q, R and S are the positions of four garden statues in a park. PQRS is a quadrilateral. Scale: 1 : 25 000

1. Construct the locus of points equidistant from the line segments $PS$ and $PQ$.

Draw the internal angle bisector of $\angle SPQ$.
Any point on this line is equidistant from the two line segments $PS$ and $PQ$.

2. Construct the locus of points equidistant from $P$ and $S$, then locate $A$.

Draw the perpendicular bisector of $PS$.
Any point on this line is equidistant from $P$ and $S$.

Mark the intersection of this perpendicular bisector with the angle bisector of $\angle SPQ$ as $A$.

1. Convert the actual distance $750\text{ m}$ to centimetres and apply the scale.

Scale $1:25\,000$ means

$1\text{ cm on drawing} = 25\,000\text{ cm in actual distance}$.

$750\text{ m} = 75\,000\text{ cm}$

So the distance on the scale drawing is

$\frac{75\,000}{25\,000}=3\text{ cm}.$

1. Construct the two loci that determine the position of $H$.

From $R$, draw a ray on a bearing of $315^\circ$.

Using part (b)(i), $HQ = 3\text{ cm}$, so draw an arc or circle with centre $Q$ and radius $3\text{ cm}$.

Mark the intersection of this arc with the bearing ray as $H$.