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## 'A Cartesian Puzzle' printed from http://nrich.maths.org/

We have had the following solution from Matthew, David and Jack at St. Nicolas School, Newbury. They thought there was a problem with number 6 but there isn't!

Our solutions to the missing coordinates are:

- (2,11), (0,9), (2,7) ..............(4,9)

which had both rotational and line symmetry.
- (3,7), (3,4), (8,4) ..............(8,7)

which had both rotational and line symmetry.
- (18,3), (16,5), (12,5) ..............(10,3)

which had line symmetry.
- (13,12), (15,14), (12,17) ..............(10,15)

which had both rotational and line symmetry.
- (7,14), (6,11), (7,8) ..............(8,11)

which had both rotational and line symmetry.
- (15,9), (19,9), (16,11) ..............(12,11)

which had rotational symmetry.
- (11,3), (15,2), (16,6) ..............(12,7)

which had both rotational and line symmetry.
- (9,16), (2,9), (9,2) ..............(16,9)

which had both rotational and line symmetry.

We plotted these 8 sets of coordinates, which made a symmetrical star.

We also heard from George and Thalia from Hoyle Court Primary School, Baildon who worked together to complete the puzzle. Their teacher wrote:
They worked out the missing co-ordinates for the quadrilaterals then tried to produce the final symmetrical shape.

At first their shape was not symmetrical. They realised it should be a star and corrected the two inaccurate co-ordinates.

Then went back and drew the original two quadrilaterals again using the amended co-ordinates from the star.

Great teamwork!!

Here are photos of their symmetrical star and some of their initial quadrilaterals: