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Enlargements
2.4 Transformation Geometry
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.
Picture
Point
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
• 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.
Slide Projector
Design
Better?

• In this case, the
  light bulb is the
  centre of
  enlargement!

• C. of E. is the point
  from which the E. is
  constructed.
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
In Action
 http://www.ngfl-cymru.org.uk/vtc/ngfl/maths/
echalk/enlargement/intro/enlargementIntro.html
• 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!
Enlarging - Grid
Enlarging - Grid

Step 1
Enlarging - Grid

Step 1
Enlarging - Grid

Step 1       Step 2
Enlarging - Grid

Step 1       Step 2
Enlarging - Grid

Step 1       Step 2   Step 3
Enlarging - Grid

Step 1       Step 2   Step 3
Ray Method
   Video
Very Useful
Very Useful

Step 1
Very Useful

Step 1
Very Useful

Step 1




Step 2
Very Useful

Step 1




Step 2
Step 3
Step 3
Step 3   Step 4
Step 3   Step 4
Step 3                     Step 4




In this example the scale factor is 3 that’s why
     every length is being multiplied by 3!
Step 5
Step 5
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
To Find the Centre of the
      Enlargement
• 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.
What is an enlargement?

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Enlargements - Strand 2

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