SOLUTION: Unit transformations homework 4 rotations on the ... - Free Printable

Let's solve the rotation problems step by step using the given figure and coordinate rules for rotations on the coordinate plane.

We are given a rectangle with vertices:

- A(2,7)
- B(7,7)
- C(7,1)
- D(2,1)

We'll use standard rotation rules around the origin (0,0):

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🔁 Rotation Rules:

- 90° clockwise: $(x, y) \rightarrow (y, -x)$
- 90° counterclockwise: $(x, y) \rightarrow (-y, x)$
- 180°: $(x, y) \rightarrow (-x, -y)$
- 270° clockwise = 90° counterclockwise: $(x, y) \rightarrow (-y, x)$
- 270° counterclockwise = 90° clockwise: $(x, y) \rightarrow (y, -x)$

Now let’s solve each question.

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1. Find A' after A is rotated 90° clockwise

Point A: (2, 7)

Apply 90° clockwise rule: $(x, y) \rightarrow (y, -x)$
So: $(2, 7) \rightarrow (7, -2)$

✔ Answer: (7, -2)

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2. Find B' after B is rotated 90° clockwise

Point B: (7, 7)

$(7, 7) \rightarrow (7, -7)$

✔ Answer: (7, -7)

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3. Find C' after C is rotated 180° clockwise

Point C: (7, 1)

180° rotation: $(x, y) \rightarrow (-x, -y)$
So: $(7, 1) \rightarrow (-7, -1)$

✔ Answer: (-7, -1)

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4. Find D' after D is rotated 90° clockwise

Point D: (2, 1)

Apply 90° clockwise: $(x, y) \rightarrow (y, -x)$
So: $(2, 1) \rightarrow (1, -2)$

✔ Answer: (1, -2)

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5. Find A' after A is rotated 180° counterclockwise

Rotation of 180° counterclockwise is same as 180° clockwise: $(x, y) \rightarrow (-x, -y)$

A: (2, 7) → (-2, -7)

✔ Answer: (-2, -7)

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6. Find B' after B is rotated 270° counterclockwise

270° counterclockwise = 90° clockwise (since 270° CCW = 90° CW)

Use rule: $(x, y) \rightarrow (y, -x)$

B: (7, 7) → (7, -7)

✔ Answer: (7, -7)

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✔ Final Answers Matched to Questions:

| Question | Answer |
|--------|--------|
| 1. A' after 90° clockwise | (7, -2) |
| 2. B' after 90° clockwise | (7, -7) |
| 3. C' after 180° clockwise | (-7, -1) |
| 4. D' after 90° clockwise | (1, -2) |
| 5. A' after 180° CCW | (-2, -7) |
| 6. B' after 270° CCW | (7, -7) |

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Now, you're told to "match your answers in the table to solve the riddle." Although the riddle isn't shown here, typically these types of worksheets assign letters to coordinates or have a word puzzle based on the answers.

But since the answers match exactly what was provided in the image (and the problem seems self-consistent), we can confirm that all six answers are correct.

✔️ Final Answer Summary:

1. (7, -2)
2. (7, -7)
3. (-7, -1)
4. (1, -2)
5. (-2, -7)
6. (7, -7)

These should be used to fill in the table and decode the riddle (e.g., matching coordinates to letters). Let me know if you'd like help decoding the riddle once you have the full table!