An enlargement is a transformation that changes the size and position of a shape. It has two key components: 1. A center of enlargement, which is the point from which the enlargement is constructed. 2. A scale factor, denoted by k, which is the number by which the object is enlarged. All lengths of the shape are multiplied by the scale factor, while angles remain unchanged. The area of the enlarged shape is equal to k^2 times the original area.

1. Enlargements
2.4 Transformation Geometry

2. Transformation
• is when a shape’s size or position is
changed or transformed.
• the original shape is the OBJECT.
• the changed shape is the
transformation.

3. Picture

4. Point

5. We learn
about
enlargements!
An enlargement changes the SIZE and the POSITION
of a shape!
To enlarge a shape we need TWO things!
1. A centre or enlargement
2. A scale factor

6. • When a shape is enlarged, ALL lengths
are multiplied by the scale factor and all
angles remain UNCHANGED.
• An an example of use is a slide
projector.

7. Slide Projector
Design

8. Better?
• In this case, the
light bulb is the
centre of
enlargement!
• C. of E. is the point
from which the E. is
constructed.

9. The Scale Factor
• Is denoted by the
Let’s see it in action!
letter ‘k’ in the new
course.
• It is the number by
which the object is fun enlargements
enlarged.
http://www.ngfl-cymru.org.uk/vtc/ngfl/maths/echalk/enlargement/intro/enlargementIntro.html

10. In Action
http://www.ngfl-cymru.org.uk/vtc/ngfl/maths/
echalk/enlargement/intro/enlargementIntro.html

11. • Important to note that while
enlargements normally enlarge shapes
you can also decrease, reduce or make
shapes smaller.
• For example if k = 1/2 then your shape
would be half the original size!

12. Enlarging - Grid

13. Enlarging - Grid
Step 1

14. Enlarging - Grid
Step 1

15. Enlarging - Grid
Step 1 Step 2

16. Enlarging - Grid
Step 1 Step 2

17. Enlarging - Grid
Step 1 Step 2 Step 3

18. Enlarging - Grid
Step 1 Step 2 Step 3

19. Ray Method
Video

20. Very Useful

21. Very Useful
Step 1

22. Very Useful
Step 1

23. Very Useful
Step 1
Step 2

24. Very Useful
Step 1
Step 2

26. Step 3

27. Step 3

28. Step 3 Step 4

29. Step 3 Step 4

30. Step 3 Step 4
In this example the scale factor is 3 that’s why
every length is being multiplied by 3!

32. Step 5

33. Step 5

34. Properties of enlargements
• Shape of image is the same only size
has changed.
• Angle measures remain the same.
• Image length = k (object length) OR
• k = Image length/Object length
• Area of Image = k^2 (area object) OR
• k^2 = Area of Image/Area of object

35. To Find the Centre of the
Enlargement

36. • 1. Choose two points on the image and
their corresponding points on the
original figure.
• 2. From each of these points on the
larger figure, draw a line to the
corresponding point on the smaller
figure.
• 3. Produce these lines until they
intersect at the point is the centre of the
enlargement.

38. What is an enlargement?