Transformation Tease

What are the coordinates of this shape after it has been transformed in the ways described? Compare these with the original coordinates. What do you notice about the numbers?

Coordinate Patterns

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

Ten Hidden Squares

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

Spiral Snail

Stage: 2 and 3 Short Challenge Level:

A sheet of graph paper is placed with its x-axis pointing due East and its y-axis pointing due North. A sluggish snail starts at point (0,0) and slowly, but smoothly, slithers 1 unit North, 2 units East, 3 units South, 4 units West, 5 units North, 6 units East, 7 units South, 8 units West, 9 units North and (lastly!) 10 units East.

At which point does the snail finally arrive?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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