Negative enlargements

An enlargement with a negative scale factor is similar to a positive enlargement, but with an added twist: the shape is flipped across the centre of enlargement. The shape still changes in size, but the negative scale factor means the shape is reflected as well as enlarged or reduced.

Key Concepts

• Centre of Enlargement: The point from which the shape is enlarged and reflected. Every point on the shape is stretched or compressed along a straight line passing through this centre.
• Negative Scale Factor: A negative scale factor causes a reflection as well as an enlargement or reduction. The magnitude (absolute value) of the scale factor still determines how much bigger or smaller the shape becomes, while the negative sign causes the shape to flip over the centre of enlargement.

How to Perform an Enlargement with a Negative Scale Factor

1. Identify the centre of enlargement. This is the point from which all points of the shape will be enlarged and reflected.
2. Determine the scale factor. If the scale factor is negative, it means the shape will be reflected across the centre of enlargement and either enlarged (if the magnitude is greater than 1) or reduced (if the magnitude is between 0 and 1).
3. For each point on the shape, draw a line from the centre of enlargement to the point.
4. Measure the distance from the centre of enlargement to the point. Multiply this distance by the absolute value of the scale factor to find the new distance.
5. Move the point along the line, but in the opposite direction of the original position, to reflect it across the centre. Then place the new point at the calculated distance.
6. Repeat the process for all points of the shape to find the enlarged and reflected shape.