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

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Presentation transcript:

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

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 preimage.

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'.

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

Dilation Simulation

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

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 = Scalar factor = 0.93

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’(_____,_____)

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.

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.

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’(_____,_____)