1. Dilations

2. SWBAT: Graph dilations SWBAT: Determine the scale factor of a dilation

3. 4 Types of Transformations
translations
Reflections
Rotations
Dilations

4. New Vocabulary: DIlation
DILATION: A transformation where the figure and its image are similar.
Reduced picture of the original
Original
Enlarged picture of the original

5. New Vocabulary: Scale Factor
SCALE FACTOR: How much you are going to grow or shrink the original figure.
Scale factor: length of new figure = 6 = 1
same side of old figure A A’ 16 8 8 4 B C B’ 12 C’
DILATION 6
ORIGINAL

6. Enlarged Vs. Reduced
ENLARGED: when the scale factor is > 1 (the shape will get bigger). REDUCED: when the scale factor is <1 (the shape will get smaller).

7. WILL IT BE ENLARGED OR REDUCED?
Recall: Scale factor > 1 = enlarged
Scale factor < 1 = reduced
Scale factor = 3
Scale factor = 5/2
Scale factor = ½
Scale factor = 3/2
Scale factor = 9
Scale factor = 1/8

8. WILL IT BE ENLARGED OR REDUCED?
Recall: Scale factor > 1 = enlarged
Scale factor < 1 = reduced
Scale factor = Enlarged
Scale factor = 5/2 Enlarged
Scale factor = ½ Reduced
Scale factor = 3/2 Enlarged
Scale factor = Enlarged
Scale factor = 1/8 Reduced

9. Finding a Dilation
Scale factor: corresponding side of dilation (new figure) corresponding side of original figure (old figure) Step 1: List all the coordinates of a figure Step 2: Multiply ALL coordinates of the original by the scale factor to get the dilation

10. Dilation on Graphs: Example 1
DILATE PENTAGON PQRST BY A SCALE FACTOR OF 2. P: (-5, 3) x2 = P’ = (-10, 6) Q: (0, 4) x2 = Q’ = (0, 8) R: (4, 2) x2 = R’ = (8, 4) S: (2, -3) x2 = S’ = (4, -6) T: (-4, -3) x2 = T’ = (-8, -6)

11. Dilation on Graphs: Example 2
DILATE PENTAGON PQRST BY A SCALE FACTOR OF 7. P: (-5, 3) Q: (0, 4) R: (4, 2) S: (2, -3) T: (-4, -3)

12. Dilation on Graphs: ANSWERS
DILATE PENTAGON PQRST BY A SCALE FACTOR OF 7. P: (-5, 3) x7 = P’ = (-35, 21) Q: (0, 4) x7 = Q’ = (0, 28) R: (4, 2) x7 = R’ = (28, 14) S: (2, -3) x7 = S’ = (14, -21) T: (-4, -3) x7 = T’ = (-28, -21)

13. YOU TRY
Dilate by a scale factor of ½
Dilate by a scale factor of 4
Dilate by a scale factor of ¾
Dilate by a scale factor of 5
Dilate by a scale factor of 3
P (0, 9) Q (6, 9) R(6, 0) S(0, 0)

14. YOU TRY: ANSWERS P (0, 9) Q (6, 9) R(6, 0) S(0, 0)

15. Find the scale factor from the original and the dilation
Scale factor = image original
P (0, 9) Q (6, 9) R(6, 0) S(0, 0)
P’(6, 0) Q’(3, 6)
R’(3, 0) S’(0, 0)
Choose 1 set of non-zero x-coordinates to compare: P’ Q’ R’

16. Find the scale factor from the original and the dilationP’
Scale factor = image original Q’
P (0, 9) Q (12, 18) R(12, 0) S(0, 0)
P’(6, 0) Q’(3, 6)
R’(3, 0) S’(0, 0)
Choose 1 set of non-zero x-coordinates to compare: R’

17. Please try the classwork with your table groups
YOU TRY:
Please try the classwork with your table groups