Loci

Teachers' Notes

The content of this programme has been chosen to demonstrate the main types of loci that are tested in examinations at Intermediate Level GCSE. The loci are introduced within real contexts but abstract geometrical constructions are also demonstrated. The loci that are specifically covered are:

• locus of points a constant distance from a given point
  
• locus of points a constant distance from a given line
  
• locus of points equidistant from two parallel lines
  
• locus of points equidistant from two converging lines
  
• locus of points equidistant from two given points

The programme could be used as an introduction to the topic or to provide enrichment alongside classroom teaching. Some investigative work on creating paths according to a rule would be useful prior to viewing. Drawing techniques using compasses are demonstrated and these include the angle bisector and the perpendicular bisector. Students need not have met these before, but it is assumed that they will have the opportunity to draw these themselves. The use of maps with simple scales is covered in context. The concept of regions is introduced, but this could be extended by further work on regions and intersecting loci after viewing.

The programme would be useful as a revision tool and it could also be used to consolidate knowledge at the end of teaching the topic. Some students may benefit from viewing short sections of the programme as they progress through stages of the work and then view the entire programme to summarise the main points.

The answers to Worksheet 1 could be used as the basis for a discussion after viewing. For revision purposes, students may find it useful to have their own copy of the Key Facts and Exam Tips section of these notes. These could be edited and amended to meet individual needs.