Enlargement worksheet for geometry transformations, featuring four shapes to be enlarged on a grid with specified scale factors.

Let's solve each of the four enlargement problems step by step. Since I can't draw directly on the image, I will explain how to enlarge each shape using the given scale factor and centre of enlargement, and describe where the new enlarged shape should be drawn.

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🔷 What is Enlargement?

Enlargement is a transformation that changes the size of a shape using a scale factor from a fixed point called the centre of enlargement.

To perform an enlargement:
1. Measure the distance from the centre of enlargement to each vertex of the shape.
2. Multiply this distance by the scale factor.
3. Plot the new points in the same direction from the centre.
4. Connect the new points to form the enlarged shape.

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## ✔ Problem 1: Scale Factor 2

- Shape: Green triangle
- Centre of enlargement: Green 'x' (bottom-left of the triangle)
- Scale factor: 2

Step-by-step:

1. The green triangle has vertices at:
- Bottom-left: (say) (2, 5)
- Bottom-right: (4, 5)
- Top: (3, 8)

2. Centre of enlargement is at (2, 4) — just below the triangle.

3. For each vertex, find vector from centre to vertex:
- From (2,4) to (2,5): up 1 → ×2 = up 2 → new point: (2,6)
- From (2,4) to (4,5): right 2, up 1 → ×2 = right 4, up 2 → (6,6)
- From (2,4) to (3,8): right 1, up 4 → ×2 = right 2, up 8 → (4,12)

4. New triangle vertices: (2,6), (6,6), (4,12)

> ✔ Draw a triangle with these points — it will be twice as big and above the original.

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## ✔ Problem 2: Scale Factor 4

- Shape: Blue rectangle
- Centre of enlargement: Blue 'x' (top-left of the grid)
- Scale factor: 4

Step-by-step:

1. Rectangle is 2×1 squares: say vertices at:
- (9,10), (11,10), (11,11), (9,11)

2. Centre of enlargement: (7,13)

3. Find vectors from centre to each vertex:
- (9,10): right 2, down 3 → ×4 = right 8, down 12 → (15,1)
- (11,10): right 4, down 3 → ×4 = right 16, down 12 → (23,1)
- (11,11): right 4, down 2 → ×4 = right 16, down 8 → (23,5)
- (9,11): right 2, down 2 → ×4 = right 8, down 8 → (15,5)

4. New rectangle: (15,1), (23,1), (23,5), (15,5)

> ✔ This will be a large rectangle far to the right and down from the original.

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## ✔ Problem 3: Scale Factor 3

- Shape: Purple square
- Centre of enlargement: Purple 'x' (inside the square)
- Scale factor: 3

Step-by-step:

1. Square is 3×3 units, centred at the 'x'. Let’s assume:
- Vertices: (5,10), (8,10), (8,13), (5,13)
- Centre of enlargement: (6.5,11.5) — middle of square

2. But since it's on grid, let’s use coordinates:
- Assume the purple 'x' is at (7,11) — inside the square.

3. Measure from (7,11) to each corner:
- (5,10): left 2, down 1 → ×3 = left 6, down 3 → (1,8)
- (8,10): right 1, down 1 → ×3 = right 3, down 3 → (10,8)
- (8,13): right 1, up 2 → ×3 = right 3, up 6 → (10,17)
- (5,13): left 2, up 2 → ×3 = left 6, up 6 → (1,17)

4. New square: (1,8), (10,8), (10,17), (1,17)

> ✔ This will be a much larger square, stretched out from the centre.

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## ✔ Problem 4: Scale Factor ½

- Shape: Pink trapezium
- Centre of enlargement: Pink 'x' (far right, bottom-right corner)
- Scale factor: ½ (reduction)

Step-by-step:

1. Trapezium base: 6 units wide, top: 4 units, height: 4 units
- Approximate vertices:
- Bottom-left: (10,5)
- Bottom-right: (16,5)
- Top-right: (14,9)
- Top-left: (12,9)

2. Centre of enlargement: (18,4) — bottom-right outside

3. Vectors from centre to each vertex:
- (10,5): left 8, up 1 → ×½ = left 4, up 0.5 → (14,4.5)
- (16,5): left 2, up 1 → ×½ = left 1, up 0.5 → (17,4.5)
- (14,9): left 4, up 5 → ×½ = left 2, up 2.5 → (16,6.5)
- (12,9): left 6, up 5 → ×½ = left 3, up 2.5 → (15,6.5)

4. New trapezium vertices: (14,4.5), (17,4.5), (16,6.5), (15,6.5)

> ✔ This will be a smaller trapezium, half the size, located closer to the centre (pink x).

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✔ Summary of How to Draw Each:

| Problem | Shape | Scale Factor | New Size | Location |
|--------|-------|--------------|----------|---------|
| 1 | Triangle | 2 | Double size | Above and slightly right of original |
| 2 | Rectangle | 4 | 4× bigger | Far right and down |
| 3 | Square | 3 | 3× bigger | Larger square around centre |
| 4 | Trapezium | ½ | Half size | Closer to pink 'x', smaller |

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📌 Tips for Drawing:

- Use a ruler to draw lines from the centre of enlargement through each vertex.
- Mark the new points at the scaled distances.
- Connect the new points to form the enlarged shape.

You can now complete the worksheet by drawing the new shapes based on these calculations!

Let me know if you'd like a visual sketch description or coordinate table!