Problem number two. Isabel rotates the hexagonal sheet of paper as shown. Each rotation turns the hexagon through the same angle in the same direction. The figure shows the result of one rotation. Which of these numbers of rotations would leave the sheet looking as it did at the start? Let's look at the hexagon and see what happens to the triangles as we rotate it multiple times. That's the original hexagon after one, two, and three rotations. We can see that the triangles of the hexagon move one space clockwise after every rotation. And that means that to get all the triangles back to where they did at the start, we would need to do six rotations, since there are six spaces in the hexagon. However, none of the options equal six. But we can see that after we do six rotations, we'll be back to the start. And then we can do six more rotations and we will be back to the start again, for the exact same reason. That means that after six plus six rotations, or twelve rotations, we will again be back to the sheet looking as it did at the start. Which means that the only option that works is E, twelve.

hexagon

rotation

triangles

clockwise

twelve