Investigation

Problem

The lines given by the following four equations enclose a square.

1. $y-2=x$

2. $y+x=6$

3. $y=x-1$

4. $y+x-3=0$

You might like to convince yourself of this before going any further!

• Given any three of the four lines that enclose a square, can you find the other one?
• You are given the area of the square and the coordinates of one vertex. Can you find possible equations of the four lines enclosing it?
• What is a minimal amount of information needed to be able to describe the equations of the four lines enclosing a square?

You might like to use the following scenarios as starting points for your investigation.

You might like to try a graphical approach to this problem, perhaps using Desmos or GeoGebra.