Transformations Worksheets (Geometry) | Cazoom Maths - 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, determine its new position after rotation.
3. Plot the rotated points and connect them to form the rotated image.

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🧩 Step-by-Step Method

#### ✔ Steps to Rotate a Shape:
1. Locate the center of rotation (X) on the grid.
2. Identify coordinates of each vertex of the shape.
3. Apply the rotation rule:
- 90° clockwise:
$(x, y) \rightarrow (y, -x)$
- 90° counterclockwise:
$(x, y) \rightarrow (-y, x)$
- 180°:
$(x, y) \rightarrow (-x, -y)$
- 270° clockwise (or 90° counterclockwise):
$(x, y) \rightarrow (-y, x)$
4. Plot the new points and draw the rotated shape.

> ⚠️ Note: These formulas assume the center of rotation is at the origin (0,0). If X is not at the origin, you must:
> - Translate the shape so that X moves to the origin.
> - Apply the rotation.
> - Translate back.

But since this is a grid-based worksheet, you can use visual counting instead of formulas.

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🔍 Example (Visual Approach)

Suppose in problem #1:
- A triangle has vertices at (2, 5), (4, 5), and (3, 3).
- Point X is at (3, 4).
- Rotation: 90° clockwise about X.

You would:
1. Measure the vector from X to each vertex.
2. Rotate that vector 90° clockwise.
3. Add it back to X’s position to get the new point.

For example:
- From X(3,4) to (2,5): vector = (-1, 1)
- Rotate 90° clockwise: (1, 1) → becomes (1, 1)? Wait — let's correct:

✔ Rotation Rule for 90° Clockwise:
$(x, y) \rightarrow (y, -x)$

So vector $(-1, 1)$ becomes $(1, 1)$ → then add to X:
New point = (3 + 1, 4 + 1) = (4, 5)

Repeat for all vertices.

But again, if you're doing this on graph paper, just count squares:
- Move from X to the point.
- Turn 90° clockwise and go same distance.

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📝 General Tips for Each Problem

| Problem | Rotation | Strategy |
|--------|----------|---------|
| 1 | 90° clockwise | Use visual turn; check distances from X |
| 2 | 90° clockwise | Same as above |
| 3 | 90° clockwise | Be careful with orientation |
| 4 | 90° counterclockwise | Opposite direction |
| 5 | 90° counterclockwise | Use reverse turn |
| 6 | 90° counterclockwise | Watch direction |
| 7 | 180° | Flip over X; opposite side |
| 8 | 180° | Same as above |
| 9 | 180° | Center symmetry |
| 10 | 90° clockwise | Again, clockwise turn |
| 11 | 90° clockwise | L-shape – rotate carefully |
| 12 | 90° counterclockwise | U-shape – pay attention to corners |

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✔ Final Answer Format (How to Fill It In)

For each question:
- Draw the rotated shape on the grid.
- Ensure all vertices are correctly placed.
- The shape should be the same size and shape, just turned.

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🛠 Tools You Can Use

- Use tracing paper or a transparent overlay to rotate.
- Or use a protractor to measure angles.
- Count grid squares from X to each vertex, then apply rotation.

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If you can describe one of the problems (e.g., “Problem 1: blue triangle, point X at (3,4), rotate 90° clockwise”), I can help you solve it step-by-step!

Otherwise, the best way to complete this worksheet is:
1. Carefully identify point X.
2. For each shape, rotate every corner using the rules.
3. Connect the dots.

Would you like me to walk through one specific problem from the worksheet? Just describe it!