Try to approach the problem systematically.

As you go along try to understand why the graph takes the shape that it does:

- by relating it to the rolling polygon and the journey of the dot
- by trying to predict what will happen before you set the polygon rolling

Could the dot have been on the centre of a polygon?

Try for each of the polygons.

Could the dot have been on the centre of the base of a polygon?

Try for each of the polygons.

Could the dot have been on the centre of one of the sloping sides of a polygon?

Try for each of the polygons.

Could the dot have been on the centre of a side opposite the base of a polygon?

Try for each of the polygons.

Could the dot have been on a vertex opposite the base of a polygon?

Try for each of the polygons.

Could the dot have been on a vertex on the base of a polygon?

Try for each of the polygons...

Alternatively...

- try all possible positions of the dot in a triangle,
- and then in a square,
- and then in a pentagon,
- and then in a hexagon...