The lines given by the following four equations enclose a square.
\(y-2=x\)
\(y+x=6\)
\(y=x-1\)
\(y+x-3=0\)
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.
