1. Entry Task 1. Translate the triangle with vertices A(2, –1), B(4, 3), and C(–5, 4) along the vector. 2. Given the points (-3,2) and (6,-1) reflect them across the line x=2 and find their image. A'(4,1), B'(6, 5),C(–3, 6) (7,2) and (-2,-1)

2. LT – I understand dilation images of figures. Success Criteria - I can Identify and draw dilations. Chapter 9.6 Dilations Learning Target

3. Dilation – a similarity transformation with a center (c) and scale factor (n) in which a figure is enlarged or reduced without altering the center A dilation is not an isometry. Center of dilation – the point that the scale factor is based at Enlargement – scale factor is greater than 1 Reduction – scale factor is less than 1 Vocabulary

4. Note that a dilation is a transformation that changes the size of a figure but not the shape. The image and the preimage of a figure under a dilation are similar but not equal. A dilation is NOT an isometry. Click HereHere

5. Example 1: Identifying Dilations Tell whether each transformation appears to be a dilation. Explain. A. B. Yes; the figures are similar and the image is not turned or flipped. No; the figures are not similar.

6. 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.

7. Example 1: Quadrilateral ABCD has vertices A(-2, -1), B(-2, 1), C(2, 1) and D(1, -1). Find the coordinates of the image for the dilation with a scale factor of 2 and center of dilation at the origin. A B C A’ B’ C’ D D’

9. Example 2: Drawing Dilations Copy the figure and the center of dilation P. Draw the image of ∆WXYZ under a dilation with a scale factor of 2. Step 1 Draw a line through P and each vertex. Step 2 On each line, mark twice the distance from P to the vertex. Step 3 Connect the vertices of the image. W’W’X’X’ Z’Z’ Y’Y’

10. Check It Out! Example 2 Copy the figure and the center of dilation. Draw the dilation of RSTU using center Q and a scale factor of 3. Step 1 Draw a line through Q and each vertex. Step 2 On each line, mark twice the distance from Q to the vertex. Step 3 Connect the vertices of the image. R’R’ S’S’ T’T’ U’U’

11. Finding a Scale Factor The blue triangle is a dilation image of the red triangle. Describe the dilation. The center is X. The image is larger than the preimage, so the dilation is an enlargement.

12. New over Old When we want to find a scale factor, simply find two corresponding side lengths and create a fraction with the new length over the old. Then reduce if needed. Example What is the scale factor? Let’s assume EFG is the new, the the scale factor is 8/4 or 2. If we assume ABC is the new then we have 4/8 or ½.

13. Homework Homework p. 590 7-33 odds

14. Graphing Dilation Images ∆PZG has vertices P(2,0), Z(-1, ½), and G (1, -2). What are the coordinates of the image of P for a dilation with center (0,0) and scale factor 3? a) (5, 3) b) (6,0) c) (2/3, 0)d) (3, -6)

15. Graphing Dilation Images Solution: The scale factor is 3, so use the rule: (x, y)  (3x, 3y). P(2,0)  P’(32, 30) or P’(6, 0). The correct answer is B. What are the coordinates for G’ and Z’?

16. Finding a Scale Factor The blue quadrilateral is a dilation image of the red quadrilateral. Describe the dilation.

17. Lesson Quiz: Part I 1. Tell whether the transformation appears to be a dilation. yes 2. Copy ∆RST and the center of dilation. Draw the image of ∆RST under a dilation with a scale of.

18. 3. A rectangle on a transparency has length 6cm and width 4 cm and with 4 cm. On the transparency 1 cm represents 12 cm on the projection. Find the perimeter of the rectangle in the projection. Lesson Quiz: Part II 4. Draw the image of the triangle with vertices E(2, 1), F(1, 2), and G(–2, 2) under a dilation with a scale factor of –2 centered at the origin. 240 cm