KS3 and KS4 Transformations Worksheets - Transformations of Graphs ... - Free Printable

Since I can't view or access images directly, I can’t see the specific shapes or their positions on the grid. However, I can guide you through how to solve rotation problems like the ones in your worksheet titled *"Rotation (A)"*, and help you understand the process step by step.

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🔷 What is Rotation?

Rotation is a transformation that turns a shape around a fixed point (called the center of rotation) by a certain angle and direction (clockwise or counterclockwise).

In this worksheet:
- You are rotating each shape about a marked point labeled X.
- The rotations are typically by 90°, 180°, or 270°, either clockwise or anti-clockwise.
- You need to draw the new position of the shape after rotation.

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✔ Steps to Rotate a Shape

1. Identify the center of rotation (X) — This is the fixed point around which everything rotates.
2. Find the coordinates of each vertex of the shape.
3. Apply the rotation rules based on the angle and direction:
- For a 90° clockwise rotation around the origin:
$(x, y) \rightarrow (y, -x)$
- For a 90° anti-clockwise rotation:
$(x, y) \rightarrow (-y, x)$
- For a 180° rotation:
$(x, y) \rightarrow (-x, -y)$
- For a 270° clockwise (same as 90° anti-clockwise):
$(x, y) \rightarrow (-y, x)$

> ⚠️ But since the rotation is not necessarily around the origin, but around point X, you must translate the shape so that X becomes the origin, apply the rotation, then translate back.

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🔄 Step-by-step Method for Rotating Around Point X

Let’s say:
- Point $ X $ has coordinates $ (a, b) $
- A vertex of the shape is at $ (x, y) $

Step 1: Translate the point so that X is at the origin:
$ (x - a, y - b) $

Step 2: Apply the rotation rule:

| Rotation | Rule |
|--------|------|
| 90° clockwise | $ (x', y') \rightarrow (y', -x') $ |
| 90° anti-clockwise | $ (x', y') \rightarrow (-y', x') $ |
| 180° | $ (x', y') \rightarrow (-x', -y') $ |
| 270° clockwise | $ (x', y') \rightarrow (-y', x') $ |

Step 3: Translate back by adding $ (a, b) $:
New point = $ (new_x + a, new_y + b) $

Repeat for all vertices, then draw the rotated shape.

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💡 Example (Hypothetical)

Suppose:
- Point X is at $ (3, 2) $
- A triangle has a vertex at $ (5, 4) $
- We want to rotate it 90° clockwise about X

Step 1: Translate:
$ (5 - 3, 4 - 2) = (2, 2) $

Step 2: 90° clockwise:
$ (2, 2) \rightarrow (2, -2) $

Step 3: Translate back:
$ (2 + 3, -2 + 2) = (5, 0) $

So the new vertex is at $ (5, 0) $

Repeat for other vertices and draw the rotated shape.

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🔍 How to Solve Each Question in Your Worksheet

For each problem (1–12):
1. Identify the center of rotation (X).
2. Note the angle and direction.
3. Pick each corner of the shape.
4. Use the method above to find the new positions.
5. Draw the rotated shape on the grid.

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🧩 Tips for Accuracy

- Use tracing paper or a protractor if allowed.
- Mark the original and rotated points clearly.
- Check that distances from X remain the same (rotation preserves distance).
- The orientation changes depending on direction.

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📌 Final Advice

If you describe one of the problems (e.g., “Problem 1: Blue triangle, 90° clockwise about X”), I can walk you through solving it exactly.

Alternatively, if you can describe the coordinates of the shape and point X, I can compute the rotated image.

Let me know which question you'd like help with!