In this worksheet, you are asked to rotate shapes about the origin by different angles. Let's go through the rotation steps for each of the given figures:

1) 180° rotation

• For a 180° rotation, each point $(x, y)$ becomes $(-x, -y)$.
• You need to apply this transformation to every vertex of the shape.

2) 90° clockwise rotation

• For a 90° clockwise rotation, each point $(x, y)$ becomes $(y, -x)$.

3) 90° counterclockwise rotation

• For a 90° counterclockwise rotation, each point $(x, y)$ becomes $(-y, x)$.

4) 180° rotation

• Same rule as number 1 applies. Every point $(x, y)$ becomes $(-x, -y)$.

5) 90° clockwise rotation

• Use the same rule as number 2. Transform $(x, y)$ into $(y, -x)$.

6) 90° counterclockwise rotation

• Use the same rule as number 3. Every $(x, y)$ transforms into $(-y, x)$.

7) 180° rotation

• Use the same rule as numbers 1 and 4. Points $(x, y)$ will become $(-x, -y)$.

8) 90° clockwise rotation

• Use the same rule as numbers 2 and 5, where $(x, y)$ turns into $(y, -x)$.

Once you apply these transformations, you can graph each shape in its new position.

Would you like detailed steps for one of the rotations or have any questions?

Here are some related questions you can explore:

1. What happens to a shape when it's rotated by 270° clockwise?
2. How does a 360° rotation affect the position of a shape?
3. How do rotations affect the orientation of a shape (e.g., clockwise vs counterclockwise)?
4. Can you identify any symmetry after rotating certain shapes?
5. How do reflections differ from rotations in terms of transformation?

Tip: When rotating, it can be helpful to first visualize what happens to the points at the corners of the shape before plotting the whole figure.