1 / 18

Warm Up

Identify and Perform Dilations. Warm Up. Lesson Presentation. Lesson Quiz. If ABC ~ DEF, find each value. 25. 36. 5. ANSWER. ANSWER. ANSWER. 5. 2. Warm-Up. 1. EF. 2. AC. 3. scale factor. a. Because = , the scale factor is k = .

arden-young
Download Presentation

Warm Up

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Identify and Perform Dilations Warm Up Lesson Presentation Lesson Quiz

  2. If ABC ~ DEF, find each value. 25 36 5 ANSWER ANSWER ANSWER 5 2 Warm-Up 1.EF 2.AC 3.scale factor

  3. a. Because = , the scale factor is k = . The image P’ is an enlargement. a. CP’ 12 3 CP 8 2 Example 1 Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. SOLUTION

  4. b. b. Because = , the scale factor is k = . The image P’ is a reduction. CP’ 3 CP 5 18 30’ Example 1 Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. SOLUTION

  5. Draw and label DEFG. Then construct a dilation of DEFGwith point Das the center of dilation and a scale factor of 2. Example 2 SOLUTION STEP 1 Draw DEFG. Draw rays from Dthrough vertices E, F, and G.

  6. Open the compass to the length of DE. Locate E’ on DEsoDE’ = 2(DE). Locate F’ and G’ the same way. Example 2 STEP 2

  7. Example 2 STEP 3 Add a second label D’ to point D. Draw the sides ofD’E’F’G’.

  8. 1. In a dilation, CP’ = 3 and CP = 12. Tell whether the dilation is a reduction or an enlargement and find its scale factor. ANSWER Because = , the scale factor is k = . The image P’ is a reduction. CP’ 1 CP 4 3 12 Guided Practice

  9. 2. Draw and label RST. Then construct a dilation of RSTwith Ras the center of dilation and a scale factor of 3. ANSWER Guided Practice

  10. Simplify the product: 4 [ ] 4(3) 4(0) 4(1) = 4 4(2) 4(– 1) 4(– 3) [ ] [ ] [ ] 12 0 4 3 0 1 3 0 1 = 8 – 4 –12 2 – 1 – 3 2 – 1 – 3 Example 3 SOLUTION Multiply each element in the matrix by 4. Simplify.

  11. [ ] 2 1 –10 3. 5 4. 3 – 4 7 [ ] – 4 1 0 –2 ANSWER 9 – 5 –7 [ ] [ ] 10 5 –50 8 –2 0 –18 10 14 15 – 20 35 ANSWER Guided Practice Simplify the product.

  12. The vertices of quadrilateral KLMNare K(– 6, 6), L(– 3,6), M(0, 3), and N(– 6, 0). Use scalar multiplication to find the image of KLMNafter a dilation with its center at the origin and a scale factor of . Graph KLMNand its image. K L M N K′L′ M′ N′ [ ] [ ] –2 –1 0 –2 2 2 1 0 = 1 1 3 3 Image matrix Scale factor Polygon matrix –6 –3 0 –6 6 6 3 0 Example 4 SOLUTION

  13. The vertices of ABCare A(– 4, 1),B(– 2, 2), and C( – 2,1). Find the image of ABCafter the given composition. Translation: (x, y) (x + 5, y + 1) Dilation: centered at the origin with a scale factor of 2 STEP 1 Graph the preimage ABCon the coordinate plane. Example 5 SOLUTION

  14. STEP 2 Translate ABC5 units to the right and 1 unit up. Label it A’B’C’. STEP 3 Dilate A’B’C’using the origin as the center and a scale factor of 2 to find A”B”C”. Example 5

  15. 5. The vertices of RSTare R(1, 2), S(2, 1), and T(2, 2). Use scalar multiplication to find the vertices of R’S’T’ after a dilation with its center at the origin and a scale factor of 2. ANSWER R′(2,4), S′(4,2), T′(4,4) Guided Practice

  16. 6. A segment has the endpoints C( –1, 1) and D(1, 1). Find the image of CDafter a 90° rotation about the origin followed by a dilation with its center at the origin and a scale factor of 2. ANSWER C′(–2, –2), D′(–2, 2) Guided Practice

  17. Find the scale factor. Tell whether the dilation is reduction or an enlargement. Find the value of x. 1. 5 3 ANSWER ; enlargement ; 1.2 Lesson Quiz

  18. Find the image matrix that represents a dilation of XYZ with vertices X(3,2), Y(8,–1) and Z(–1,–1) centered at the origin with scale factor . Then graph the polygon and its image. 2. ANSWER 1 2 Lesson Quiz

More Related