Enlargement in Maths definition
Enlargement in maths is a transformation that changes the size of a shape. The shape can become larger or smaller, but it keeps the same basic shape. When a shape is enlarged, all lengths are multiplied by the same scale factor. The original shape is often called the object, and the new shape after the transformation is called the image.
The scale factor tells you how much the shape changes in size. If the scale factor is 2, every side length becomes twice as long. If the scale factor is 3, every side length becomes three times as long. If the scale factor is 1 over 2, the shape becomes smaller and every side length is halved. The angles stay the same, so the original shape and the enlarged shape are similar.
Enlargement is used in geometry, transformations, coordinate grids, ratio, proportion, scale drawings, maps, plans and similar shapes. At GCSE level, students are often asked to enlarge a shape from a centre of enlargement, find the scale factor, describe an enlargement fully, or work out missing lengths in similar shapes. Enlargement also links to real-life scaling, such as drawings of buildings, models, photographs and maps.
A centre of enlargement is the fixed point from which the enlargement is measured. If a point on the original shape is 4 squares from the centre and the scale factor is 2, the matching point on the enlarged shape will be 8 squares from the centre in the same direction. This is why drawing lines from the centre of enlargement through the original vertices can help students construct the image accurately.
For example, suppose a triangle has side lengths 3 cm, 4 cm and 5 cm. If it is enlarged by scale factor 2, the new side lengths are 6 cm, 8 cm and 10 cm. The triangle is bigger, but the angles have not changed. If the same triangle is enlarged by scale factor 1 over 3, the new side lengths are 1 cm, 4 over 3 cm and 5 over 3 cm. This type of enlargement reduces the size of the shape.
Negative scale factors can also appear in higher GCSE questions. A negative scale factor places the image on the opposite side of the centre of enlargement. For example, a scale factor of -2 means the image is twice as large, but it is positioned through the centre on the opposite side. This can be more difficult because students must think about direction as well as size.
Enlargement affects area differently from length. If lengths are enlarged by scale factor 3, the area is enlarged by scale factor 9 because 3 times 3 equals 9. For volume, the scale factor is cubed. This is important in similar shapes and compound measure questions. Students should not assume that area changes by the same factor as length.
A full description of an enlargement should include the scale factor and the centre of enlargement. Related ideas include transformations, translation, rotation, reflection, similar shapes, ratio, proportion, scale drawings, coordinates and vectors. Understanding enlargement helps students see how shapes can change size in a controlled and predictable way, which is useful in both exam geometry and real-world scale problems.