Introduction to Enlargement
Enlargement is a transformation that changes a shape's size. You multiply every length by a scale factor, so a factor of 2 turns a 4 cm side into 8 cm. It grows or shrinks from a fixed point called the centre of enlargement.
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What Is Enlargement?
- Enlargement is a transformation that changes the size of a shape.
- All angles stay the same after an enlargement, but the lengths get bigger or smaller.
Understanding the Scale Factor
- The scale factor is the number you multiply all lengths by.
- If the scale factor is greater than 1, the shape gets bigger, and if it is between 0 and 1, the shape gets smaller.
How to Enlarge a Shape from a Centre
- Draw straight lines from the centre of enlargement to each corner.
- Measure the distance from the centre to a corner, then mark the new point 3 times as far from the centre.
Finding the Centre of Enlargement
- Join each corner of the original shape to the matching corner of the enlarged shape.
- Extend the lines until they meet at one point, called the centre of enlargement.
Finding the Scale Factor
- The scale factor is found using new length ÷ original length.
- If a side goes from 4 units to 8 units, then , so the scale factor is 2.
- Exam tip: Choose any pair of matching sides. Horizontal or vertical lines on the grid are easiest.
Practice Questions
Test your understanding
A square has sides of length . After an enlargement with scale factor 2, what is the length of each side of the new square?
Correct! 🎉 +10 pointsNot quite right
Multiply the original length by the scale factor: . So the new side length is .
If a shape is enlarged by a scale factor between 0 and 1, what happens to its size?
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A scale factor between 0 and 1 makes the shape smaller.
The original length of a rectangle is . After enlargement, the length is . What is the scale factor?
Correct! 🎉 +20 pointsNot quite right
Use the formula: scale factor .
A square is enlarged by scale factor 3. The original width is . What is the area after enlargement?
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First, find the new width: . Now, .
On a grid, a rectangle has one corner at (3, 2). It is enlarged by scale factor 3 from the origin. Where is the matching corner of the new rectangle?
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To enlarge from the origin, multiply both numbers in (3, 2) by 3. , . So the new corner is at (9, 6).
On a grid, a shape has a vertex at (2, 5). It is enlarged by scale factor 4 from the point (1, 2). Where is the matching vertex after enlargement?
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First, see how far (2, 5) is from the centre (1, 2). It’s 1 across and 3 up. Multiply both by 4: , . Start at (1, 2), go 4 across and 12 up. You get (5, 14). So the new vertex is at (5, 14).
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Interactive Activity
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Students Also Ask
The questions students bump into most on this topic
When you enlarge a shape, the angles stay exactly the same. Only the lengths change, because every length is multiplied by the scale factor. This is why an enlarged shape keeps the same overall proportions as the original and simply looks larger or smaller.
No. An enlargement only makes a shape bigger when the scale factor is greater than 1. If the scale factor is between 0 and 1, the shape gets smaller instead. For example, a scale factor of one half halves every length, so the shape shrinks.
The formula is: scale factor = new length ÷ original length. Choose any pair of corresponding lengths. Take one from the original shape and the matching one from the enlarged shape, then divide. For example, a new length of 8 divided by an original length of 4 gives a scale factor of 2.
To find the centre of enlargement, draw a straight line through each pair of corresponding corners on the two shapes. Extend the lines until they cross. The single point where all the lines meet is the centre of enlargement. Every corner of the shape lines up with this point.
You need two things to describe an enlargement: the scale factor and the centre of enlargement. The scale factor is the number you multiply every length by, which sets the new size. The centre of enlargement is the fixed point the enlargement is made from.