1. 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