It gives an opportunity for experimentation and making your own
conjecture, which then needs to be proved. Three different
methods of proof are based on coordinates, vectors and complex
numbers.
Key questions
Four points are vertices of a parallelogram. What do you know
about the line segments joining them?
If on a line segment you draw a square:
- what do you know about the vertices of the square?
- can you find the coordinates, or the position vector of
the centre of the square?
Possible
support