1. Bellwork  Perform a glide reflection of and over line y=x for the points A: (-4,2), B:(-22,-3) and C:( 0,2) No Clickers

2. Bellwork Solution  Perform a glide reflection of and over line y=x for the points A: (-4,2), B:(-22,-3) and C:( 0,2)

3. Section 9.7

5. The Concept  For our last section of chapter 9 we’re going to revisit Dilations  For the most part, our understanding of these transformations was relatively complete. We are primarily going to revisit the process and discuss how we can perform dilations with matrices

6. Review Dilations Dilations Scaling of an object by the same factor in all directions Scaling of an object by the same factor in all directions Similarity transformation Similarity transformation Not an Isometry Not an Isometry

7. Coordinate Notation For similicity, we prefer to be able to notate for dilations For similicity, we prefer to be able to notate for dilations For dilations centered at the origin For dilations centered at the origin (x,y)  (kx,ky), where k is a scale factor (x,y)  (kx,ky), where k is a scale factor If 0<k<1, reduction If 0<k<1, reduction If k>1, enlargement If k>1, enlargement We can also find k from two objects by dividing the length of a side of the image by the length of the corresponding side of the preimage We can also find k from two objects by dividing the length of a side of the image by the length of the corresponding side of the preimage

8. Drawing a Dilation Draw a dilation of an object with vertices (4,6), (2, 4) & (6,-6) using a scale factor of 1/2 Draw a dilation of an object with vertices (4,6), (2, 4) & (6,-6) using a scale factor of 1/2

9. Example Draw a dilation of scale factor 2 for ABCD with vertices A(2,2), B(4,2), C(4,0), D(0,-2).

10. Scalar Multiplication Because in a dilation all coordinates are scaled by the same number we can use a process called scalar multiplication of a matrix to show the new coordinates Because in a dilation all coordinates are scaled by the same number we can use a process called scalar multiplication of a matrix to show the new coordinates Scalar multiplication is the “distribution” of a value to interior values of a matrix Scalar multiplication is the “distribution” of a value to interior values of a matrix e.g. a dilation of scale factor 4 on the previous set of points e.g. a dilation of scale factor 4 on the previous set of points Scale factor

11. Example We can also combine transformations We can also combine transformations Perform a combination of transformations by translating over the vector then dilating by a factor of ½. Perform a combination of transformations by translating over the vector then dilating by a factor of ½. A: (3,1), B: (2,0), C: (-2,5) A: (3,1), B: (2,0), C: (-2,5)

12. Homework  9.7 Exercises 1-6, 15-22, 26, 36, 37

13. Most Important Points  Definition of Dilation  Bounds for the k scalar  Performing Dilations  Using scalar multiplication to perform dilations  Combining transformations