Enlargements
Grade 5What an enlargement does
An enlargement changes the size of a shape by a scale factor, measured from a fixed centre of enlargement. All lengths in the image are the original lengths multiplied by the scale factor. Angles stay the same — the shape is similar to the original.
Scale factors to know
Scale factor greater than 1: image is larger. Scale factor between 0 and 1: image is smaller (but still called an enlargement). Negative scale factor: image is on the opposite side of the centre and is also flipped.
To draw an enlargement: draw a ray from the centre of enlargement through each vertex. Multiply the distance from the centre to each vertex by the scale factor, and mark the new vertex along the ray at that new distance.
Worked example — finding the scale factor
EXAMPLE
A shape has a side of length 4 cm. After an enlargement, the corresponding side is 10 cm. The centre of enlargement is at the origin, and an original vertex is at (2, 3). Find the scale factor and the image vertex.
Scale factor = 10 ÷ 4 = 2.5. Image vertex = (2 × 2.5, 3 × 2.5) = scale factor 2.5; image vertex (5, 7.5).
Describing an enlargement
To describe an enlargement fully: state "enlargement", give the scale factor, and give the coordinates of the centre of enlargement. All three pieces are needed for full marks.
