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### Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

### Symmetry Challenge

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

### Hidden Meaning

What is the missing symbol? Can you decode this in a similar way?

# A Cartesian Puzzle

##### Stage: 2 Challenge Level:

Here are the coordinates of some quadrilaterals but in each case one coordinate is missing!
1. $(2,11), \; (0,9),\; (2,7),\; (?,?)$
2. $(3,7),\; (3,4),\; (8,4),\; (?,?)$
3. $(18,3),\; (16,5), \;(12,5),\; (?,?)$
4. $(13,12),\; (15,14),\; (12,17),\; (?,?)$
5. $(7,14),\; (6,11),\; (7,8),\; (?,?)$
6. $(15,9),\; (19,9),\; (16,11),\; (?,?)$
7. $(11,3),\; (15,2),\; (16,6),\; (?,?)$
8. $(9,16),\; (2,9),\; (9,2),\; (?,?)$

The quadrilaterals are all symmetrical. This may be rotational or line symmetry or both. Can you work out what the missing coordinates are if you know they are all positive? Is there more than one way to find out?

Now plot those eight missing coordinates on a graph like this. What shape do they make and what sort of symmetry does it have?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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