Worksheet on coordinate plane rotations with a rectangle and rotation questions.

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

Note: 180° counterclockwise = same as 180° clockwise = $(-x, -y)$

Point A: (2, 7) → $(-2, -7)$

✔ Answer: (-2, -7)

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

270° counterclockwise = same as 90° clockwise (because 270° CCW = 90° CW)

So apply 90° clockwise rule: $(x, y) \rightarrow (y, -x)$

Point B: (7, 7) → $(7, -7)$

✔ Answer: (7, -7)

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✔ Final Answers Matched to the Table:

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

All answers match the provided solutions in the image.

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🧩 Now, the riddle:

The instructions say: "Match your answers in the table to solve the riddle."

But the riddle itself isn’t visible in the image you provided.

However, since all the coordinates have been correctly calculated and matched, if this is a puzzle where you plug in answers into letters or clues (like a cryptogram), then the correct answers are:

- (7, -2)
- (7, -7)
- (-7, -1)
- (1, -2)
- (-2, -7)
- (7, -7)

If you can provide the actual riddle or how the answers map to letters, I can help decode it.

But based on the math, all answers are correct as shown.

✔ Final Check: All transformations are correct.