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# Attractive Rotations

##### Age 11 to 14 Challenge Level:

Take a look at the image below. How do you think it was created? Did you notice any symmetry in the image?

Here is a diagram which shows how we created the image. We started with a triangle (shaded) and then used the coordinate grid to help us to rotate it through multiples of $90^{\circ}$ around the point $(0,0)$. Create some images of your own by rotating a shape through multiples of $90^{\circ}$.
You might like to start with a triangle as we did, or you might want to use other shapes.

How can you use a coordinate grid to help you to rotate each vertex around $(0,0)$?
What is the relationship between the coordinates of the vertices as they rotate through multiples of $90^{\circ}$?

Here are some more ideas to explore:

Can you use an isometric grid to rotate a shape through multiples of $60^{\circ}$?

Try creating some images based on other rotations, such as $30^{\circ}$ or $72^{\circ}$ or... (you will need to use a protractor for these). What is the rotational symmetry of your final image if you rotate through multiples of $80^{\circ}$ or $135^{\circ}$? Can you explain why?