Enlargements | Mathematics for GCSE/IGCSE - Year 11 PDF Download

Enlargement

• Enlargement is a transformation altering the size of a shape.
  • The scale factor indicates the multiplier for each side's enlargement compared to the original.
  • A scale factor exceeding 1 enlarges the image, making it larger than the original.
  • A scale factor below 1 reduces the image, making it smaller than the original.
• Enlargement alters the position of a shape.
• The orientation of the shape remains unchanged in a positive enlargement.

How do I enlarge a shape?

• Definition: Enlargement involves resizing a shape on a coordinate grid.
• Procedure:
  • Step 1: Begin from the center of enlargement and calculate the horizontal and vertical distances to a vertex on the original object.
  • Step 2: Multiply these distances by the provided scale factor.
  • Step 3: Starting from the center of enlargement again, determine the new distances and plot the position of the corresponding vertex on the grid of the enlarged image. The distances will point in the same direction for a positive scale factor and the opposite direction for a negative scale factor.
  • Step 4: Repeat Steps 1 to 3 for the remaining vertices.
  • Step 5: Connect the vertices on the enlarged image and label it.

How do I describe an enlargement?

• You should recognize and explain an enlargement when shown one.
• A complete description of a transformation is necessary for maximum points.
• For an enlargement, ensure you:
  • Identify it as an enlargement.
  • Specify the scale factor.
  • Provide the coordinates of the center of enlargement.

Negative Enlargements

How do I enlarge a shape if it has a negative scale factor?

• Enlargements with negative scale factors are still relevant, though less common for identification.
• The procedure for negative scale factor enlargements parallels that of positive ones. However, note the following:
  • The object's orientation changes as a negative enlargement involves a 180-degree rotation.
  • When measuring the distance between the center of enlargement (CoE) and the enlarged image, it's measured on the opposite side of the CoE.