This module covers drawing with a pair of compasses and a ruler: the perpendicular bisector of a line, the bisector of an angle, and the locus (the set of all points that obey a rule). It then combines two loci to find the points that satisfy both rules at once.
Check the current Cambridge IGCSE Mathematics 0580 syllabus for the exact wording of each content point in your exam year. The drawing habits taught here stay the same across versions. Our Mathematics learning guide shows where this module sits among the others.
What should you already know?
You need to measure and draw lengths and angles with a ruler and protractor, and to recognise a circle, a radius and a right angle. Pythagoras’ theorem helps for the checking steps, but you can meet it as you go. Geometry facts from angles and geometric reasoning are a useful companion.
An orienting example
Points A and B are 6 cm apart. Find the points that are exactly 5 cm from both A and B.
Step 1, name the loci: points 5 cm from A lie on a circle of radius 5 cm centred at A. The same is true for B. The answer is where the two circles cross.
Step 2, locate them: the crossing points are equidistant from A and B, so they lie on the perpendicular bisector of AB. The midpoint M is 3 cm from each end.
Step 3, use Pythagoras: in triangle AMP, AM = 3 and AP = 5, so MP² = 25 − 9 = 16 and MP = 4.
Answer: two points, each 4 cm from the midpoint, one on each side of AB.
Check: the distance from A to P is √(3² + 4²) = √25 = 5, and the same holds from B. Both conditions are met.
That single question used a circle locus, a perpendicular bisector and a check against the original rule. It is a good picture of how the module fits together.
In which order should you study it?
- Construct a perpendicular bisector accurately: the tool for “equidistant from two points”.
- Construct an angle bisector: the tool for “equidistant from two lines”.
- Describe a locus using distance conditions: turns a sentence about distance into a shape.
- Combine two loci to locate feasible positions: finds where two rules overlap.
- Check a construction against the original constraints: catches slips before you hand the page in.
Then work through the mixed practice set. One lesson a day with the practice set at the weekend is a steady pace.
Which traps catch most students here?
- Changing the compass width between two arcs that were meant to be equal.
- Rubbing out construction arcs, which are the evidence that your method is correct.
- Drawing a rectangle instead of a rounded shape when a point must stay a fixed distance from a line segment.
- Treating “within” as “exactly”, so a region is drawn as a line.
- Stopping once the drawing looks right without measuring it against every condition.
Each lesson shows one of these slips in full and then corrects it.
How should you use the practice set?
Attempt each question on paper with a ruler and compasses where a drawing is useful, then open the answer. Write the reason for each step, because a method mark usually needs the reasoning as well as the drawing. The non-calculator working trainer lets you check the arithmetic in the Pythagoras steps.
When you get something wrong, read the routing notes at the end of the practice set and go back to the lesson it names. Keep a short list of your slips in the mistake log and retest queue and retry a fresh question a few days later.
If you want teaching beyond self-study, online one-to-one Mathematics tuition means an experienced teacher sees your drawing and working and finds which habit is behind the error.