Lecture Notes: Enlargements

Introduction to Enlargements

• Enlargement changes the size of a shape.
• Keeps all lengths in proportion.
• Key Concept: Scale Factor
  • Determines how much each length is multiplied.

Examples

Triangle Enlargement

• Original: Base = 2 squares, Height = 3 squares
• Double:
  • Base: 2 x 2 = 4 squares
  • Height: 3 x 2 = 6 squares
  • Scale Factor: 2
• Triple:
  • Base: 2 x 3 = 6 squares
  • Height: 3 x 3 = 9 squares
  • Scale Factor: 3

Proportion Rule

• All sides must be multiplied by the same factor for a true enlargement.
• Example of Incorrect Enlargement:
  • Base multiplied by 3, height by 2 => Not an enlargement.

Reducing Size - Still an Enlargement

• Example:
  • Trapezium original base: 8 squares shrunk to 4 squares
  • Scale Factor: 1/2
• Triangle:
  • Base from 6 squares to 2 squares
  • Scale Factor: 1/3

Exam Question Strategy

Drawing Enlargements

• Given a shape on a grid, apply scale factor.
• Example 1: Rectangle
  • Width doubled from 2 to 6 squares
  • Height tripled from 3 to 9 squares

Different Scale Factors

• Scale factor 1/2, requires dividing each dimension by 2.
• Scale factor 1/3, requires dividing each dimension by 3.

Center of Enlargement

• Determines specific location of enlarged shape.
• Example:
  • Scale factor 2, rectangle drawn with steps from point P.
  • Steps repeated equal to scale factor.

Checking Alignment

• Draw lines from center of enlargement through shape points.
• Ensure lines hit corresponding points on enlarged shape.

Reverse Enlargement

• Find scale factor by comparing dimensions.
• Identify center of enlargement by extending lines through shapes.

Coordinate Axis Enlargements

• Mark center of enlargement on grid.
• Follow steps with given scale factor.

Describing Transformations

• Types: Rotation, reflection, translation, enlargement.
• Identify enlargement by change in size.
• Determine scale factor by comparing dimensions.

Practical Applications

• Use coordinates and journey method to apply transformations.
• Calculate and apply scale factor adjustments to each side.

Conclusion

• Understanding enlargements is key for geometry and mapping transformations.
• Practice with grid examples and coordinate axes.

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