Geometric Transformation: Rotation worksheet - Free Printable

Let's solve each rotation problem step by step. We are rotating shapes about the origin (0, 0) using standard rotation rules.

---

🔁 Rotation Rules About the Origin:

- 90° Clockwise:
$(x, y) \rightarrow (y, -x)$

- 90° Counterclockwise:
$(x, y) \rightarrow (-y, x)$

- 180° Rotation:
$(x, y) \rightarrow (-x, -y)$

We'll apply these rules to each point.

---

## ✔ Problem 1: 90° Clockwise Rotation

Given triangle ABC with points:

- A = (-4, 3)
- B = (1, 4)
- C = (-1, -2)

Apply $ (x, y) \rightarrow (y, -x) $

- A' = (3, -(-4)) = (3, 4)
- B' = (4, -1)
- C' = (-2, -(-1)) = (-2, 1)

✔ Answers:
- A'(3, 4)
- B'(4, -1)
- C'(-2, 1)

---

## ✔ Problem 2: 180° Rotation

Triangle UVW:

- U = (-2, 4)
- V = (4, 3)
- W = (-3, 1)

Apply $ (x, y) \rightarrow (-x, -y) $

- U' = (2, -4)
- V' = (-4, -3)
- W' = (3, -1)

✔ Answers:
- U'(2, -4)
- V'(-4, -3)
- W'(3, -1)

---

## ✔ Problem 3: 90° Counterclockwise Rotation

Quadrilateral EFGH:

- E = (1, 1)
- F = (5, 1)
- G = (4, 4)
- H = (1, 4)

Apply $ (x, y) \rightarrow (-y, x) $

- E' = (-1, 1)
- F' = (-1, 5)
- G' = (-4, 4)
- H' = (-4, 1)

✔ Answers:
- E'(-1, 1)
- F'(-1, 5)
- G'(-4, 4)
- H'(-4, 1)

---

## ✔ Problem 4: 180° Rotation

Triangle PQR:

- P = (-2, 1)
- Q = (-2, -4)
- R = (3, -4)

Apply $ (x, y) \rightarrow (-x, -y) $

- P' = (2, -1)
- Q' = (2, 4)
- R' = (-3, 4)

✔ Answers:
- P'(2, -1)
- Q'(2, 4)
- R'(-3, 4)

---

📝 Final Answers:

#### 1.) 90° clockwise:
- A'(3, 4)
- B'(4, -1)
- C'(-2, 1)

#### 2.) 180° rotation:
- U'(2, -4)
- V'(-4, -3)
- W'(3, -1)

#### 3.) 90° counterclockwise:
- E'(-1, 1)
- F'(-1, 5)
- G'(-4, 4)
- H'(-4, 1)

#### 4.) 180° rotation:
- P'(2, -1)
- Q'(2, 4)
- R'(-3, 4)

---

✔ These are the coordinates of the images after rotation about the origin. You can now fill them into the worksheet. Let me know if you'd like a visual explanation or diagram!