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 \to + ↓ ↓ B \to + ↑ ↑ ↑ C \leftarrow \leftarrow \leftarrow + ↓ D \to A

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 \to \to \to + ↓ ↓ B or A 3 \to + 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:

$a) A 1 \to + 1 ↑ B$

$b) A 2 \to + 1 ↑ B$

$c) A 3 \to + 1 ↑ B$

$d) A 2 \to + 2 ↑ B$

$e) A 3 \to + 2 ↑ B$

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.