General Certificate of Secondary Education (GCSE) Maths Practice Exam

When enlarging a shape, the scale factor is crucial in determining how the area of the shape changes. If the scale factor is negative, the orientation of the shape changes, but it does not influence the area in terms of size—indeed, it can create a shape that is a mirror image of the original. The mathematical relationship for the area after enlargement is that it is proportional to the square of the scale factor.

For example, if the scale factor is 2, the area increases by a factor of \(2^2\) which is 4 times larger. Conversely, if the scale factor is a fraction (less than 1), the area decreases since squaring a fraction yields a smaller number. This means a constant scale factor would enable the area to be determined precisely based on the initial dimensions, despite whether the factor is less than or greater than 1.

Thus, while the scale factor may alter the shape's orientation if negative, it does not affect the calculation of area through a scale factor that plays a significant role in determining the changes in size. The correct understanding is that the area is only affected when the scale factor changes in terms of absolute value, not its sign.