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Bellwork

No Clickers. Bellwork. Perform a glide reflection of <1,4> and over line y=x for the points A: (-4,2), B :(-22,-3) and C:( 0,2). Bellwork Solution. Perform a glide reflection of <1,4> and over line y=x for the points A: (-4,2), B :(-22,-3) and C:( 0,2). Section 9.7.

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Bellwork

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

  2. Bellwork Solution • Perform a glide reflection of <1,4> and over line y=x for the points A: (-4,2), B:(-22,-3) and C:( 0,2)

  3. Section 9.7 Identify and perform Dilations

  4. Test on Tuesday

  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 • Scaling of an object by the same factor in all directions • Similarity transformation • Not an Isometry

  7. Coordinate Notation • For similicity, we prefer to be able to notate for dilations • For dilations centered at the origin • (x,y)(kx,ky), where k is a scale factor • If 0<k<1, reduction • 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

  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

  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 • 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 Scale factor

  11. Example • We can also combine transformations • Perform a combination of transformations by translating over the vector <-4,2> then dilating by a factor of ½. • 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

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