What happens to a shape when it is enlarged with a scale factor of 2?

The shape becomes twice as big. Each side length is multiplied by 2. The enlarged image is further from the centre of enlargement than the original.

What is a fractional enlargement?

An enlargement with a scale factor between 0 and 1. The image is smaller than the original and closer to the centre of enlargement.

What is the centre of enlargement?

The fixed point that determines where the enlarged image is positioned. Lines through corresponding vertices of the object and image all pass through this point.

How do you find the scale factor when describing an enlargement?

Pick a side on the original shape and the corresponding side on the enlarged image. Divide the enlarged side length by the original side length. Scale factor = new length / old length.

How do you find the centre of enlargement?

Draw straight lines through pairs of corresponding vertices (one on the original, one on the image). Repeat for several pairs. The lines intersect at the centre of enlargement.

How do you reverse an enlargement with scale factor 3?

Use an enlargement with scale factor 1/3 and the same centre of enlargement. The reciprocal of the original scale factor reverses the transformation.

If an original shape has height 3 squares and the enlarged shape has height 9 squares, what is the scale factor?

Scale factor = 9/3 = 3. The image is 3 times larger than the original.

If the scale factor is 1/2, what happens to the distance from the centre to a vertex?

The distance is halved. For example, 6 squares right becomes 3 squares right. The image is closer to the centre of enlargement.

What three pieces of information must you give to fully describe an enlargement?

1) State it is an enlargement. 2) Give the scale factor. 3) Give the coordinates of the centre of enlargement.

Enlargements | Pearson Edexcel IGCSE Maths

Q: What is the first step when enlarging a shape on a grid?

Mark the centre of enlargement. Then pick a vertex and count the horizontal and vertical distances from the centre to that vertex.

A Modular / Higher Unit 2

Vectors & Transformation Geometry

Enlargements

Summary

An enlargement is a transformation that changes the size and position of a shape by multiplying each side length by a scale factor. The centre of enlargement determines where the image is placed. Scale factors greater than 1 produce larger images; fractional scale factors between 0 and 1 produce smaller images. Understanding enlargements requires knowing how to perform them, describe them fully, and reverse them.

1. Definition and Core Concepts

An enlargement changes the size and position of a shape. The length of each side is multiplied by a scale factor.

If the scale factor is greater than 1, the enlarged image will be bigger than the original object.

If the scale factor is between 0 and 1 (fractional), the enlarged image will be smaller than the original object.

The centre of enlargement determines the position of the enlarged image. With scale factor greater than 1, the image is further from the centre; with fractional scale factor, the image is closer to the centre.

2. How to Enlarge a Shape

Step 1: Pick a vertex and count the horizontal and vertical distances from the centre of enlargement.

Step 2: Multiply both distances by the given scale factor.

Step 3: Start at the centre of enlargement and measure the new distances to find the enlarged vertex.

Step 4: Repeat for all other vertices. You may draw the enlarged shape by multiplying original lengths by the scale factor.

Step 5: Connect the vertices and label the enlarged image.

3. Describing an Enlargement

State that the transformation is an enlargement, give the scale factor (integer or fraction), and give the coordinates of the centre of enlargement.

To find the scale factor: pick a side on the original, identify the corresponding side on the image, divide the enlarged side length by the original side length.

To find the centre of enlargement: draw lines through corresponding vertices on object and image; these lines intersect at the centre of enlargement.

4. Reversing an Enlargement

An enlargement is reversed by multiplying the enlarged shape by the reciprocal of the original scale factor.

The centre of enlargement stays the same. For scale factor 3, the reverse is scale factor 1/3.

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