Ruler-and-compass constructions
Edexcel Foundation tests 5 standard constructions. The mark scheme requires:
- All construction arcs clearly visible (do not erase them).
- Use of compasses (not free-hand sketching).
- Result accurate to ±2 mm of the correct position.
A C1 (communication) mark is awarded for clean, visible arcs even before the final figure is judged.
The 5 standard constructions
1. Perpendicular bisector of a line segment AB
- Open compasses to more than half AB.
- From A, draw arcs above and below AB.
- Without changing radius, from B draw arcs that intersect the first set.
- Join the two intersection points with a straight line. This line bisects AB at 90°.
2. Bisect an angle
- From the vertex, draw an arc that crosses both arms.
- From each crossing point, draw arcs of equal radius that intersect inside the angle.
- Draw a line from the vertex through the intersection.
3. Perpendicular from a point to a line
- From the point, draw an arc that crosses the line in two places.
- From those two points, draw arcs of equal radius below the line that intersect.
- Draw a line from the original point through the intersection — perpendicular to the original line.
4. Perpendicular at a point on a line
- Choose two equidistant points on the line either side of the given point.
- From each, draw arcs of equal radius above the line that intersect.
- Join the original point to the intersection.
5. Construct a 60° angle
- Draw a line; mark a starting point A.
- From A, draw a wide arc crossing the line at B.
- From B, with the same radius, draw an arc crossing the first arc at C.
- Join A to C — angle BAC = 60°.
(Bisecting this 60° gives a 30° angle.)
Loci
Edexcel often combines constructions with loci — sets of points satisfying a condition.
- Locus equidistant from two points → perpendicular bisector.
- Locus equidistant from two intersecting lines → angle bisector.
- Locus at a fixed distance from a point → circle.
- Locus at a fixed distance from a line segment → "stadium" shape (line segments parallel to the segment, joined by semicircular ends).
Edexcel exam tip
Always leave construction arcs visible. Erasing them is the most common reason for losing the C1 mark even when the final answer is geometrically correct.
⚠Common mistakes— Common errors
- Using a protractor instead of compasses (zero marks for accuracy).
- Inconsistent arc radius across the construction.
- Joining incorrect intersection points.
- Not labelling the final construction line/point.
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