Vectors round a square

What is special about the relationships between vectors that define a square?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative




Here is a diagram showing how vectors can describe a journey round a square:

 

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Vectors round a square


The journey starts along the black vector $\pmatrix{3\cr 1}$

What vectors describe the rest of the journey?

 

There are many interesting mathematical questions about vectors that describe journeys.

Explore journeys round various squares of your own and see what you can find out.

If you would like some ideas of interesting questions to explore, take a look below.



What happens if I add vectors together?

What is special about opposite sides of the squares?

What is special about adjacent sides of the squares?

If I know the vector for the diagonal can I work out the other vectors?

   
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Vectors round a square
 

What about other shapes?