1. Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their notebooks Warm Up  1) Are the following shapes congruent?  2) If so, what type of transformation is occurring?

2. Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their notebooks

3. Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their notebooks Prior Knowledge

4. Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their notebooks What is a Dilation?  A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.  A dilation reduces or enlarges the original figure.

5. Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their notebooks What is a Dilation?  The description of a dilation includes the scale factor (or ratio) and the center of the dilation. The center of the dilation is a fixed point in the plane about which all points are reduced or enlarged. It is the only fixed point under a dilation.

6. Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their notebooks Properties of a Dilation  1) Angle measures remain the same  2) Parallel lines remain parallel.  3) Points that start on the same line stay on the same line.  4) Midpoints remain the same.  5) Letter ordering remains the same.

7. Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their notebooks Scale Factor

8. Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their notebooks Example Find the scale factor of the image

9. Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their notebooks Examples Find the scale factor in each of the images

10. Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their notebooks Dilating about a Point  If you are asked to dilate a figure containing the vertex (a, b) by a scale factor of k about the point (m, n). 1. Find the horizontal distance from a to m. 2. Multiply this horizontal distance by k. 3. Add the answer from step 2 to m and this gives you the x-coordinate of your dilation. 4. Find the vertical distance from b to n. ○ This will be positive if (a, b) is above (m, n) and will be negative if (a, b) is below. 5. Multiply this vertical distance by k. 6. Add the answer from step 5 to n and this gives you the y-coordinate of your dilation. 7. Plot your new point. 8. Repeat from all other vertices.

11. Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their notebooks Example Perform a dilation of the line segment AB centered at P with a scale factor of 2.

12. Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their notebooks Example

13. Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their notebooks Example Line segment ST and point P are shown below. The line segment undergoes a dilation by a scale factor of 1.5 through center P to produce line segment S'T'. Which of the following equations are true? Select all that apply.

14. Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their notebooks Example Guillermo claims that a dilation with a scale factor of 3 will triple the perimeter of figure. His friend asks Guillermo to show this by using the figure below where A is (-4, -2), B is (-4, 2) and C is (-1, 2). Part A: What is the perimeter of ΔABC? Part B: Apply a dilation with a scale factor of 3 about point B to find the perimeter of the new image. Is Guillermo’s claim supported?

15. Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their notebooks In the figure, the smaller shape is a dilation of the larger shape. What is the scale factor of the dilation, and what is the center of the dilation? Ascale factor: 3 ; center: (1,3) Bscale factor: 2 ; center: (−1,1) Cscale factor: 2 ; center:(0,0) Dscale factor: 112 ; center: (1,3) Escale factor: 1 ; center: (0,0) Fscale factor: 12 ; center: (1,3) Gscale factor: 12 ; center: (0,0) Hscale factor: 13 ; center: (−1,1)

16. Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their notebooks In the figure, the smaller shape is a dilation of the larger shape. What is the scale factor of the dilation, and what is the center of the dilation? Ascale factor: 3 ; center: (3,0) Bscale factor: 3 ; center: (112,−3) Cscale factor: 2 ; center: (0,0) Dscale factor: 112 ; center: (112,−3) Escale factor: 12 ; center: (0,0) Fscale factor: 12 ; center: (12,−1) Gscale factor: 13 ; center: (0,0) Hscale factor: 14 ; center: (12,−1)

17. Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their notebooks In the figure, the larger shape is a dilation of the smaller shape. What is the scale factor of the dilation, and what is the center of the dilation? Ascale factor: 3; center: (3,0) Bscale factor: 3; center: (0,0) Cscale factor: 2; center: (12,−1) Dscale factor: 112 ; center: (112,−3) Escale factor: 12 ; center: (0,0) Fscale factor: 12 ; center: (3,0) Gscale factor: 13 ; center: (0,0)

18. Essential Question: What is a dilation and how do you dilate a figure? Assessment: Students will demonstrate in writing through practice problems in their notebooks Essential Question What is a dilation and how do you dilate a figure?