Geometric Enlargements and Reductions

This page explains the fundamental principles of geometric enlargements and reductions, presenting two key properties that govern these transformations.

Definition: An enlargement or reduction with coefficient k is a geometric transformation that changes the size of a figure while maintaining its shape.

Highlight: The coefficient k determines whether the transformation is an enlargement (k>1) or a reduction (k<1).

Example: With k=1.5, an enlargement increases all lengths by a factor of 1.5, while k=0.75 reduces all lengths to 75% of their original size.

Vocabulary:

• Agrandissement: Enlargement
• Réduction: Reduction
• Coefficient: Scale factor

Property 1 demonstrates that in any enlargement or reduction:

• All lengths are multiplied by the coefficient k
• All angles remain unchanged

Property 2 shows the effect on areas and volumes:

• Surface areas are multiplied by k²
• Volumes are multiplied by k³

Example: For a figure with base area 9 units²:

• When enlarged by k=1.5: New base area = 1.5² × 9
• When reduced by k=0.75: New base area = 0.75² × 9