Position and transformation
Enlarging shapes
An enlargement makes a copy that is a different size but exactly the same shape. Every length multiplies by the scale factor — and every angle stays exactly as it was.
What an enlargement does
An ENLARGEMENT changes the lengths of a shape but keeps its PROPORTIONS. If every length on the image is twice the matching length on the object, the SCALE FACTOR is 2. Because the proportions are unchanged, the object and image are called SIMILAR SHAPES. (Similar has a precise meaning in maths: same shape, different size.)
Angles do not change
This is the part people get wrong. In an enlargement, ALL the angles stay the same size. Double every side of a triangle with a 40° angle in it and the image still has a 40° angle. Enlarging stretches lengths, not angles — that is exactly why the shape still looks the same.
Working out the image
Multiply every length by the scale factor. A triangle has a height of 1 square and a base of 2 squares. Enlarge it by scale factor 3: height: 3 × 1 = 3 squares base: 3 × 2 = 6 squares Draw those two sides on the grid, then complete the shape.
Finding the scale factor
Given an object and its image, divide a length on the IMAGE by the matching length on the OBJECT. A 4 cm side becomes 12 cm: 12 ÷ 4 = 3, so the scale factor is 3. Check it with a second pair of sides. If they give a different answer, it is not an enlargement at all.
Worked examples
A triangle 1 by 2 squares, scale factor 3
- Height: 3 × 1 = 3 squares.
- Base: 3 × 2 = 6 squares.
- Draw both, then complete the triangle.
Answer: A triangle 3 squares high and 6 squares along
A 4 cm side enlarged by scale factor 2
- Multiply the length by the scale factor.
- 4 × 2 = 8.
Answer: 8 cm
A 4 cm side becomes 12 cm — what is the scale factor?
- Divide image by object.
- 12 ÷ 4 = 3.
Answer: Scale factor 3
What happens to a 40° angle under an enlargement?
- An enlargement changes lengths only.
- The proportions, and so the angles, are unchanged.
Answer: It stays 40°
A 3 cm by 4 cm rectangle, scale factor 2
- 3 × 2 = 6 and 4 × 2 = 8.
Answer: 6 cm by 8 cm
Are the object and image congruent?
- Congruent means same shape AND same size.
- An enlargement changes the size.
Answer: No — they are similar, not congruent
Where you see this in real life
- Zooming into a photo enlarges it. Everything gets bigger together, so faces do not end up stretched.
- A dressmaker's pattern is enlarged by a scale factor for a larger size, keeping every proportion the same.
Key words
- Enlargement
- a copy of a shape at a different size, same proportions
- Scale factor
- the number every length is multiplied by
- Similar shapes
- shapes with the same proportions but different sizes
- Proportion
- the relationship between the lengths in a shape
- Corresponding
- matching — the side in the image that goes with a side in the object