\( \text{You are constructing a perpendicular bisector using compass arcs.} \)
Question 22:
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\[ \begin{aligned} &\text{The point } P \text{ lies on the line } AB. \\ &\text{Use ruler and compasses to construct an angle of } 90^{\circ} \text{ at } P. \\ &\text{You must show all your construction lines.} \end{aligned} \]
Answer:\( See construction drawing \)
Explanation:
\begin{aligned} &\text{Place the compass at point } P \text{ and draw an arc cutting } AB \text{ at two points } X \text{ and } Y. \\ &\text{From } X \text{ and } Y\text{, draw arcs of equal radius above the line so they intersect.} \\ &\text{Draw a straight line from } P \text{ through the intersection; this is perpendicular to } AB \text{ at } P \,(90^\circ). \end{aligned}