Enlargements (Leaving Cert Mathematics): Revision Notes
📚 Revision Notes
Enlargements
What is Enlargement?
Enlargement changes the size of a shape while preserving its proportions. Each side of the shape is multiplied by the same scale factor, which determines how much bigger or smaller the shape becomes.
Key Points:
- Scale Factor Greater than : The shape gets larger.
- Scale Factor Between and : The shape gets smaller.
- Negative Scale Factor: The shape is enlarged and also flipped (reflected).
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Examples:
- If the scale factor is , the new shape will be three times as large.
- If the scale factor is , the new shape will be half the size of the original
Describing Enlargements
To fully describe an enlargement, you must provide:
- Centre of Enlargement: The fixed point from which the shape is enlarged. This is usually given as a coordinate.
- Scale Factor of the Enlargement: This tells you how much the shape has been enlarged or reduced.
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Worked Example 1: Enlarging a Shape
Given:
- Centre of Enlargement: ()
- Scale Factor: Steps:
- Draw lines from the centre of enlargement through each vertex (corner) of the blue object.
- Measure the distance from the centre of enlargement to each vertex of the blue shape.
- Double the distance to find where the vertices of the purple shape should be, as the scale factor is .
- Plot the new points and draw the enlarged purple shape. Notice: The distance of each point in the purple shape from the centre of enlargement is twice that of the corresponding point on the blue shape.
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Worked Example 2: Reducing a Shape (Fractional Scale Factor)
Given:
- Centre of Enlargement: ()
- Scale Factor: Steps:
- Draw lines from the centre of enlargement through each vertex of the blue object.
- Measure the distance from the centre of enlargement to each vertex of the blue shape.
- Reduce the distance by a factor of to find where the vertices of the purple shape should be.
- Plot the new points and draw the reduced purple shape. Notice: Since the shape got smaller, the scale factor is fractional (less than ). Each point on the purple shape is one-third the distance from the centre of enlargement as the corresponding point on the blue shape.
