2. Check It Out! Example 1 a.b. Yes, the figures are similar and the image is not turned or flipped. No, the figures are not similar. Tell whether each transformation appears to be a dilation. Explain.

4. Example 4: Drawing Dilations in the Coordinate Plane

5. Example 4 Continued Graph the preimage and image. P’ Q’ R’ P R Q

6. Success Criteria:  I can identify rigid motion  I can name images and corresponding part Today’s Agenda 9.4 Composition of Isometries Understand how to identify and draw compositions of transformations.  Do now (Dilations)  Check HW  Lesson 9.4  HW #36  Perf Task (Groups) on Monday and Test on Tuesday

8. The glide reflection that maps ∆JKL to ∆J’K’L’ is the composition of a translation along followed by a reflection across line l. A composition of transformations is one transformation followed by another. For example, a glide reflection is the composition of a translation and a reflection across a line parallel to the translation vector.

9. The image after each transformation is congruent to the previous image. By the Transitive Property of Congruence, the final image is congruent to the preimage. This leads to the following theorem. Theorem

10. Example 1: Drawing Compositions of Isometries Draw the result of the composition of isometries. K L M

11. Example 1 Continued Step 1 The rotational image of (x, y) is (–x, –y). K(4, –1)  K’(–4, 1), L(5, –2)  L’(–5, 2), and M(1, –4)  M’(–1, 4). Step 2 The reflection image of (x, y) is (–x, y). K’(–4, 1)  K”(4, 1), L’(–5, 2)  L”(5, 2), and M’(–1, 4)  M”(1, 4). K L M M’ K’ L’ L” M” K”

12. Check It Out! Example 2 L KJ

13. L KJ L'’ J’’ K’’ K’ J’ L’ Check It Out! Example 2 Continued Step 2 The rotational image of (x, y) is (–x, –y). J’(1, 2)J”(-1, -2), K’(4, 2)K”(-4, -2), and L’(3, 0)L”(-3, 0). Step 1 The reflection image of (x, y) is (x, -y). J(1, –2) J’(1, 2), K(4, –2) K’(4, 2), and L(3, 0) L’(3, 0).

14. Theorem

15. Check It Out! Example 2 Find the image of the shape after the transformation LMNP  L”M”N”P”translation: LM PN L’ M’ P’ N’ L”M” P”N” l m

16. You Try PQR has vertices P(5, –2), Q(1, –4), and R(–3, 3). P”(3, 1), Q”(–1, 3), R”(–5, –4) P”(5, 2), Q”(1, 4), R”(-3, -3)

17. Assignment #36 pg 574 #6,8, 12-15, 23,24

18. Success Criteria:  I can identify rigid motion  I can name images and corresponding parts Today’s Agenda Do Now: Determine the coordinates of the image of P(-3, 5) under each transformation. 9.4 Composition of Isometries Understand how to identify and draw compositions of transformations.  Do now  Check HW  New chapter 9.4 1. a translation 2 units right and 4 units down 2. a rotation of 270° about the origin (-1, 1) (5, 3) 3. a reflection across the x-axis (–3, –5)