Rotations and Reflections on the Coordinate Plane Worksheet | Fun ... - Free Printable

Since I can't view or access uploaded images directly, I can't see the specific image you're referring to. However, based on your description, it appears to be a geometry worksheet titled "Rotation (A)", where students are asked to rotate various shapes around a marked point X on a grid.

Let me walk you through how to solve such rotation problems and provide general guidance for each type of rotation:

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🔷 Understanding Rotations

Rotating a shape means turning it around a fixed point (called the center of rotation, here labeled X) by a certain angle and direction.

Common rotations:
- 90° clockwise
- 90° counterclockwise
- 180° (either direction)
- 270° clockwise / 90° counterclockwise (same result)

The key is to:
1. Identify the center of rotation (X).
2. For each vertex of the shape:
- Measure its position relative to X.
- Apply the rotation rules.
- Plot the new position.
3. Connect the rotated points to form the new shape.

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🔷 Rotation Rules (Using Coordinates)

Assume the center of rotation is at point $ X = (a, b) $. To rotate a point $ P = (x, y) $:

#### ✔ 90° Clockwise:
$$
(x', y') = (a + (y - b), b - (x - a))
$$

#### ✔ 90° Counterclockwise:
$$
(x', y') = (a - (y - b), b + (x - a))
$$

#### ✔ 180°:
$$
(x', y') = (2a - x, 2b - y)
$$

#### ✔ 270° Clockwise (or 90° CCW):
Same as 90° counterclockwise.

> 💡 Tip: If the center of rotation is the origin (0,0), formulas simplify:
> - 90° CW: $ (x, y) \to (y, -x) $
> - 90° CCW: $ (x, y) \to (-y, x) $
> - 180°: $ (x, y) \to (-x, -y) $

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🔷 Step-by-Step Instructions for Each Problem

For each numbered problem (1–12), follow these steps:

1. Locate point X on the grid — this is your pivot.
2. Identify coordinates of all vertices of the shape.
3. Apply the correct rotation rule based on the instruction (e.g., 90° clockwise).
4. Plot the new points after rotation.
5. Draw the rotated shape with the same size and orientation but turned.

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🔷 Example (Problem 1)

Suppose:
- Shape is a triangle with vertices at A(2,6), B(4,4), C(3,2)
- Point X is at (3,4)
- Rotate 90° clockwise about X

Use the formula:
$$
(x', y') = (a + (y - b), b - (x - a))
$$

For point A(2,6):
- $ x' = 3 + (6 - 4) = 3 + 2 = 5 $
- $ y' = 4 - (2 - 3) = 4 - (-1) = 5 $
→ New point: (5,5)

Repeat for B and C, then connect the new points.

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🔷 General Tips

- Use tracing paper or a protractor if allowed.
- Check that distances from X remain the same (rotation preserves size).
- The orientation changes: clockwise vs counterclockwise matters!

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📌 Final Answer Format

Since I can’t see the actual image, I can’t draw or give exact coordinates. But if you describe one of the problems (e.g., “Problem 1: blue triangle, 90° clockwise about X”), I can help solve it step by step.

Alternatively, if you want, you can:
- Describe the shape and location of X.
- Tell me which rotation is required.
- I’ll guide you through plotting the rotated shape.

Would you like to do that?