Scale Factors and Centres of Enlargement (B) Worksheet | Fun and ... - Free Printable

Problem Overview:

The task involves enlarging given shapes using specific scale factors from the centre of enlargement marked by an "×". The scale factors provided are:
1. Scale Factor = -1
2. Scale Factor = -2
3. Scale Factor = -1/2

We need to understand how these scale factors affect the shapes and then apply them correctly.

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Key Concepts:

1. Scale Factor:
- A positive scale factor enlarges or reduces the shape while maintaining its orientation.
- A negative scale factor enlarges or reduces the shape but also reflects it across the centre of enlargement.
- The magnitude of the scale factor determines the size change (e.g., 2 means twice as large, 0.5 means half as large).

2. Centre of Enlargement:
- All points on the shape are moved away from or towards this point based on the scale factor.
- For a negative scale factor, the shape is reflected across this point.

3. Steps to Enlarge a Shape:
- Identify the coordinates of each vertex of the shape relative to the centre of enlargement.
- Multiply these coordinates by the scale factor.
- Plot the new coordinates to draw the enlarged shape.

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Solution for Each Part:

#### Part 1: Scale Factor = -1
- Shape A: Green triangle
- Centre of Enlargement: Marked by "×" near the triangle.
- Effect of Scale Factor = -1:
- This will reflect the shape across the centre of enlargement and maintain its size (since the magnitude is 1).
- Each vertex of the triangle will be mirrored across the centre of enlargement.

Steps:
1. Identify the vertices of the green triangle relative to the centre of enlargement.
2. Multiply their coordinates by -1.
3. Plot the new vertices and connect them to form the reflected triangle.

Result:
The enlarged shape will be a triangle of the same size as the original but flipped across the centre of enlargement.

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#### Part 2: Scale Factor = -2
- Shapes C and D:
- Shape C: Blue triangle
- Shape D: Orange parallelogram
- Centres of Enlargement: Marked by "×" near each shape.
- Effect of Scale Factor = -2:
- This will reflect the shapes across the centre of enlargement and double their size (since the magnitude is 2).

Steps:
1. Identify the vertices of each shape relative to their respective centres of enlargement.
2. Multiply their coordinates by -2.
3. Plot the new vertices and connect them to form the enlarged shapes.

Result:
- Shape C: The blue triangle will be reflected and doubled in size.
- Shape D: The orange parallelogram will be reflected and doubled in size.

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#### Part 3: Scale Factor = -1/2
- Shapes E and F:
- Shape E: Purple pentagon
- Shape F: Pink arrow
- Centres of Enlargement: Marked by "×" near each shape.
- Effect of Scale Factor = -1/2:
- This will reflect the shapes across the centre of enlargement and reduce their size to half (since the magnitude is 1/2).

Steps:
1. Identify the vertices of each shape relative to their respective centres of enlargement.
2. Multiply their coordinates by -1/2.
3. Plot the new vertices and connect them to form the enlarged shapes.

Result:
- Shape E: The purple pentagon will be reflected and reduced to half its size.
- Shape F: The pink arrow will be reflected and reduced to half its size.

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Final Answer:

The solution involves applying the scale factors as described above to each shape. The final enlarged shapes will be:
1. Shape A: Reflected across the centre of enlargement (Scale Factor = -1).
2. Shape C: Reflected and doubled in size (Scale Factor = -2).
3. Shape D: Reflected and doubled in size (Scale Factor = -2).
4. Shape E: Reflected and reduced to half its size (Scale Factor = -1/2).
5. Shape F: Reflected and reduced to half its size (Scale Factor = -1/2).

\boxed{\text{See detailed steps above for construction.}}