GCSE Maths Loci, Bearings, Constructions and Vectors: lesson and practice questions

By the end of this chapter you will be able to

• Use a scale such as 1 : 50 000 to change between distances on a map or drawing and real distances
• Construct perpendicular bisectors, angle bisectors, perpendiculars and a 60° angle with a ruler and compasses, and construct triangles from SSS, SAS and ASA
• Describe and draw loci, and shade the region that obeys several rules at once
• Measure, draw and calculate with three-figure bearings, including back bearings and journeys in two legs
• Write translations as column vectors and add, subtract, scale and find the magnitude of vectors

You should already know

• Ratio and units of length (Chapters 15 and 16)
• Angles on parallel lines and in triangles (Chapter 17)
• Pythagoras’ theorem and trigonometry (Chapter 20)
• Coordinates and translations (Chapters 12 and 21)
• Congruent triangles (Chapter 21)

Where this leads

• Circle theorems (Chapter 26, Higher)
• Vector proofs in the Higher exam, grades 8 and 9
• Plans, maps and navigation in everyday life