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Transformations: Dilations Math 8 Ms. Stewart COPY SLIDES WITH A PENCIL ICON.

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Presentation on theme: "Transformations: Dilations Math 8 Ms. Stewart COPY SLIDES WITH A PENCIL ICON."— Presentation transcript:

1 Transformations: Dilations Math 8 Ms. Stewart COPY SLIDES WITH A PENCIL ICON

2 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.

3 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'.

4 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

5 Dilation Simulation

6 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

7 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

8 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’(_____,_____)

9 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.

10 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.

11 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’(_____,_____)


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