Algebraic methods [ A3.2 Core Plenary] Here are four straight lines. The lines intersect to form a rhombus shown here in purple. Find the equations of the four straight lines. Draw some similar rhombuses and work out the equations of their lines. Is there a way of telling just by looking at the equations whether or not the lines will form a rhombus? Jot down all you can find out. Preamble This investigation gives further practice in some of the earlier work on straight line graphs set in a geometrical context. Depending on circumstances and the group, some form of graphing device (PC or calculator) might be useful but is not essential. Some children may need reminding of the properties of rhombuses. Whole-group discussion and pooling of results is very important. Possible content Interpreting and using straight lines and their equations to form rhombuses at the formers’ points of intersection. Resources Squared paper for graph grids (a graphing facility might be useful in some instances) Solution/Notes The equations for the straight lines are: y = 2x + 1, y = 2x + 5 y = -2x + 1, y = -2x + 5 Children’s own observations including: pairs of lines must be parallel (have the same x-coefficient) Original Material © Cambridge University Press 2010 Original Material © Cambridge University Press 2010