Constructions and loci · Year 11
In Year 11 you learn: regions from loci.
Constructions are accurate drawings made with a ruler and compasses only. A locus (plural loci) is the set of all points that follow a rule, such as “3 m from a post” or “the same distance from two points”, and is drawn with the same constructions.
Key facts
- Triangle from three sides: draw one side, then arcs of the other two lengths from its ends.
- Locus: all the points that obey a rule. A fixed distance from a point makes a circle.
- A fixed distance from a line makes parallel lines (with semicircles round the ends of a line segment).
- Leave construction arcs showing: they are your working.
Worked examples
Example 1
Use a ruler and compasses to construct the perpendicular bisector of the line AB.
Answer: Equal arcs from A and from B cross at two points; the line through them cuts AB in half at right angles.
Example 2
The angle AOB is 52°. Use compasses to bisect it (cut it into two equal angles).
Answer: Two angles of 26°, either side of the bisector OR.
Example 3
Construct triangle ABC with AB = 6 cm, AC = 5 cm and BC = 4 cm.
Answer: C is where an arc of radius 5 cm from A crosses an arc of radius 4 cm from B.
Example 4
A pond is a rectangle 6 m by 4 m. A fence goes round every point within 1 m of the pond. Find the area inside the fence, to 1 d.p.
Answer: 47.1 m²