1. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Section 8-1 Dilations and Scale Factors 8.1 Dilations and Scale Factors

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Terms 8.1 Dilations and Scale Factors A dilation is an example of a non-rigid transformation that preserves the shape of an object and may change its size. examples: Notation: D(x,y) = (nx, ny) Where the number n is called the scale factor scale factor = Image pre-image

3. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. 8.1 Dilations and Scale Factors 1.What is the image of the point ( -1,3) transformed by the dilation D(x,y) = (4x, 4y) What is the scale factor?

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Terms 8.1 Dilations and Scale Factors In a dilation each point and its image lie on a line that passes through a point known as the center of dilation Examples: Optics such as the iris When the iris is relatively open it is said to be dilated

5. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. lens

6. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. 2. Find the scale factor 2 cm Center of dilation 5 cm Pre-image Image

7. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. definitions If the size of a figure is reduced the dilation is called a contraction If the size of a figure is enlarged the dilation is called an expansion If n < 1, the dilation is a contraction if n > 1, the dilation is called an expansion ( n is the scale factor)

8. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. 8.1 Dilations and Scale Factors 3. Find the image of the segment with endpoints (–2, 6) and (4, 2) after the dilation D = (x, y) = 1 2 x,x, 1 2 y.   (–1, 3) (2, 1)

9. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. 8.1 Dilations and Scale Factors 4. Draw a dilation in a plane. Each point on the image is 3 times as far from the center of dilation as the corresponding point on the preimage. Dilate the triangle about A, using the scale factor 3. preimage A  image

10. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. assignment Page 502 # 1-15, 18-23, 40, 41,42, and 43