1. Dilations

2. What’s the difference??
Undilated
Dilated

3. Vocabulary
Dilation: a transformation that changes the size of a figure but NOT its shape. Similar: Two figures are similar if they have the same shape but not necessarily the same size. Scale Factor: Describes how much the figure is enlarged or reduced. Represented by the letter K You can find the image of a point by multiplying each coordinate by k.

4. To find the coordinates of the new image after a dilation:
1. Multiply each x and y-coordinate in each of the ordered pairs by the given scale factor K. 2. Then connect the vertices of the new ordered pairs.

5. Vocabulary
Enlargement: When the image is larger than the original. Multiply by a scale factor K greater than 1, K>1.

6. Vocabulary
Reduction: When the image is smaller than the original. Multiply by a scale factor K greater than 0 and smaller Than1, 0<K<1

7. Draw the image of the figure after a dilation by a scale factor of 3.
Step 1:
Label the ordered pair of each vertex.
(1,3)
(2,2)
(2,1)
(1, 1)

8. A(1,1)  (1●3, 1●3)  A’(3,3) B(2,1)  (2●3, 1●3)  B’(6,3)
Step 2:
Multiply each coordinate in the ordered pairs by the scale factor 3.
A(1,1)  (1●3, 1●3)  A’(3,3)
B(2,1)  (2●3, 1●3)  B’(6,3)
C(2,2)  (2●3, 2●3)  C’(6,6)
D(1,3)  (1●3, 3●3)  D’(3,9)

9. Plot the new points. Connect the dots to form the dilated shape.
Step 3:
Plot the new points. Connect the dots to form the dilated shape.
D’(3,9)
C’(6,6)
B’(6,3)
A’(3, 3)

10. FIND AND CLASSIFY A SCALE FACTOR
In the figure, segment X'Y' is a dilation of segment XY. Find the scale factor of the dilation and classify it as an enlargement or a reduction.
Write a ratio using the x or y-coordinate of any vertex of the dilation to the x- or y-coordinate of the corresponding vertex of the original figure.

11. Find and Classify a Scale Factor
(-4, 2) 1 2
(-2, 1)
Answer: The scale factor is . Since < 1, the dilation is a reduction.

12. STOP HERE We will cover the following information during the next class.

13. Horizontal stretch Dilate the given figure according to the rule:
(x, y) (2x, y)
Multiply X coordinates by K=2
A (-1, 2) A’ (-2, 2)
B (3, 2) B’ (6, 2)
C (3, -1) C’(6, -1)
D (-1, -1) D’ (-2, -1)
2. Graph A’ B’ C’ D’ A B D C

14. VERTICal stretch Dilate the given figure according to the rule:
(x, y) (x, 5y)
Multiply Y coordinates by K=5
A (-1, 1) A’ (-1, 5)
B (1, 1) B’ (1, 5)
C (1, -1) C’ (1, -5)
D (-1, -1) D’ (-1, -5)
2. Graph A’ B’ C’ D’ A B D C

15. Horizontal shrink A A’ B’ C’ D’ B D C

16. vertical shrink A B A’ B’ C’ D’ D C