An enlargement changes the size of a shape using a scale factor and a centre of enlargement. When the scale factor is negative, the image is resized and also rotated by half a turn about the centre.

 

 

What a Negative Scale Factor Means

A negative scale factor produces two effects at the same time.

 

The shape is enlarged or reduced depending on the size of the scale factor.

 

The shape is rotated through:
$$
180^\circ
$$
about the centre of enlargement.

 

This means the image appears on the opposite side of the centre compared to the original shape.

 

For example, a scale factor of minus two makes the shape twice as large and rotated.

 

A scale factor of minus one half makes the shape half the size and rotated.

 

The negative sign causes the half turn

 

 

Centre of Enlargement

The centre of enlargement is a fixed point that does not move.

 

Every image point lies on a straight line with the centre of enlargement and the corresponding original point.

 

With a negative scale factor, the image point lies on the opposite side of the centre from the original point.

 

 

How to Draw an Enlargement with a Negative Scale Factor

To draw an enlargement with a negative scale factor:

 

Draw the centre of enlargement clearly.

 

Draw a straight line from the centre through each vertex of the shape.

 

Measure the distance from the centre to each original point.

 

Multiply this distance by the magnitude of the scale factor.

 

Plot the new point on the opposite side of the centre.

 

Join the new points in the same order.

 

Always check the image lies across the centre

 

 

Describing an Enlargement with a Negative Scale Factor

A correct description must include:
• the scale factor, including the negative sign
• the centre of enlargement

 

For example, an enlargement with scale factor minus two and the given centre of enlargement.

 

 

Common Errors to Avoid

Common mistakes include forgetting the half turn rotation, placing the image on the same side of the centre, using the wrong distance from the centre and missing the negative sign in the description.

 

 

Key Points to Remember

A negative scale factor causes a half turn rotation about the centre.
The size change depends on the magnitude of the scale factor.
The centre of enlargement stays fixed.
Image points lie on the opposite side of the centre.
Descriptions must include the scale factor and the centre.

 

Enlargements with negative scale factors combine resizing and rotation, so careful construction and clear description are essential.