Education Technology

Advanced String Graphs Part 2

Activity Overview

This is an extension of String Graphs Part 1 but can be done independently. In this activity students stitch points on the lines y = x and y = -x. The family of straight lines form an envelope which can be modelled by finding successive points of intersection. The points of intersection can be modelled by a parabola. A range of extension questions are provided including generalising the parabola for stitching points on the lines y = mx and y = -mx.


  • Cartesian and parametric forms of lines and parabolas
  • Solutions to simultaneous equations
  • Generalisation of families of lines using parameters


  • Parameter
  • Simultaneous equations
  • Envelope

About the Lesson

This activity perfectly compliments Advanced String Graphs Part 1. The envelope created has the same form but a different equation, effectively rotated by 45 degrees. It is not essential that students complete Part 1 first, however the connection between these two activities builds towards Parts 3 and 4. Determining linear equations from two points, building a general introduces the notion of a parameter. Subsequent determination of successive points of intersection provides a set of parametric equations that can be explored. Check out the sequels: Part 3 and Part 4.