How Far Does it Move?

This problem clearly got a lot of you thinking! Several of you sent in the correct answer, including Gemma, Rachel, David, Alex, Charlie, Robert, Joel, Jamie, Carys, Soph, Bex, Rhi, Joe, Veronica, Harriet and Elspeth, all from Cowbridge Comprehensive School.

As Azeem of Mason Middle School states:

You have to have a triangle with 40 radius. Also, you must place the red dot at the bottom left corner of the triangle.

Some of you worked it out using some systematic thought and trial and error.

Sathya and Michael made a good effort at explaining how they worked this out .

Sathya from Scots College, New Zealand considered whether or not the dot could be placed in the centre of the shapes:

I first checked whether it could have been the centre of the shapes. This is impossible as it always results in a linear graph.

Sathya then went on to consider how many sides the polygon might have:

Then I checked how many segments in the line (changes in the shape of the line) and found there was 1 for every side of the shape i.e. for a pentagon 5, square 4 etc. Therefore, the graph shown had 3 segments, so I worked out it was a triangle (obviously!).

Michael from St John Payne School went a little further in exploring where the dot might be placed:

First I knew it had to be on the vertex because there was a part of the graph that was flat.
The only point at which the dot isn't travelling anywhere when the polygon is rolling is on a vertex, because then the dot is always in contact with the floor.

He then looked at the units on the graph to consider which vertex the point would be on:

We do agree! Many thanks.