Transformations: Dilations

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Transformations Dilations

• Math 8
• Ms. Stewart

COPY SLIDES WITH A PENCIL ICON
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What is a Dilation?

• A dilation is a type of transformation that
  changes the size of the image.
• We change the size of the image by using what is
  called a scalar factor.
• The scalar factor measures how much we enlarge or
  reduce the image from its pre-image.

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How do we show the dilation?

• Prime notation is used to distinguish the image
  from the pre-image. The image always has a prime
  after the letter such as A' .

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How to enlarge or reduce the size of an object

• To increase the size of an object, the scalar
  factor must be greater than 1
• To decrease the size of an object, the scalar
  factor must be less than 1

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Dilation Simulation
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How do I dilate an object?

• 1) Multiply both x and y coordinates by the
  scalar factor
• For example (x, y) (2, 4)
• Scalar factor 2
• (2 x 2 , 4 x 2)
• 2) Simplify (4, 8)
• 3) Graph new coordinates

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Reduction or Enlargement?

• State whether a dilation using the scale factor
  would result in a reduction or enlargement of the
  figure
• 1. Scalar factor 3
• 2. Scalar factor ½
• 3. Scalar factor 10
• 4. Scalar factor 0.93

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Practice Questions

• 1) Determine the image coordinates
• A(2, 2), B(2, 0) Scale factor 2
• A(_____,_____) B(_____,_____)
• 2) Determine the image coordinates
• A (2, 4), B(6, 2) Scale factor ½
• A(_____,_____) B(_____,_____)

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Practice Questions

• Determine whether the dilation from Figure A to
  Figure B is a reduction or enlargement
• Then find the values of variables m and n.

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Practice Questions

• Determine whether the dilation from Figure A to
  Figure B is a reduction or enlargement
• Then find the values of variables x, y, z.

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Warm Up Question

• 1) Determine the image coordinates
• A(1, 2), B(3, 0) Scale factor 4
• A(_____,_____) B(_____,_____)
• 2) Determine the image coordinates
• A (6, 12), B(3, 4) Scale factor ½
• A(_____,_____) B(_____,_____)