In this problem we shall use arrows to describe how to get from one point to another.

E.g.: In the diagram below we shall describe the journey from A to B to C to D and back to A as follows:


A ® + ¯ ¯ B ® + ­ ­ ­ C ¬ ¬ ¬ + ¯ D ® A
Diagram of quadrilateral

A tilted square is a square with no horizontal sides.
For example, a square with vertices at (10,10), (17,13), (14,20) and (7,17) is a tilted square.

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If AB is described as

   A ® ® ® + ¯ ¯ B    or    A 3 ® + 2 ¯ B

draw at least one square ABCD for which AB is a side. image showing points A and B



Draw squares ABCD for which one side is given below:

a)  A 1 ® + 1 ­ B

b)  A 2 ® + 1 ­ B

c)  A 3 ® + 1 ­ B

d)  A 2 ® + 2 ­ B

e)  A 3 ® + 2 ­ B

Complete the arrow notation for the squares ABCD. What do you notice?

Formulate and describe a general instruction for the construction of a square when you are given one of its sides.

Using the rule you developed above, decide whether any of the collections of points below form a square.
If so, which ones?

1. (8,3), (7,8), (2,7), (3,2)
2. (3,3), (7,4), (8,8), (4,7)
3. (16,19), (18,22), (21,20), (19,17)
4. (4,20), (21,19), (20,2), (3,3)

Explain how you decided.