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

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Presentation on theme: "SWBAT: Graph dilations SWBAT: Determine the scale factor of a dilation SWBAT."— Presentation transcript:

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

3 4 TYPES OF TRANSFORMATIONS translations Reflections Rotations Dilations

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

5 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 12 2 NEW VOCABULARY: SCALE FACTOR ORIGINAL DILATION AA’A’ B B’B’ C C’C’

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

7 Recall: Scale factor > 1 = enlarged Scale factor < 1 = reduced 1.Scale factor = 3 2.Scale factor = 5/2 3.Scale factor = ½ 4.Scale factor = 3/2 5.Scale factor = 9 6.Scale factor = 1/8 WILL IT BE ENLARGED OR REDUCED?

8 Recall: Scale factor > 1 = enlarged Scale factor < 1 = reduced 1.Scale factor = 3 Enlarged 2.Scale factor = 5/2 Enlarged 3.Scale factor = ½ Reduced 4.Scale factor = 3/2 Enlarged 5.Scale factor = 9 Enlarged 6.Scale factor = 1/8 Reduced WILL IT BE ENLARGED OR REDUCED?

9 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 FINDING A DILATION

10 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) DILATION ON GRAPHS: EXAMPLE 1

11 DILATE PENTAGON PQRST BY A SCALE FACTOR OF 7. P: (-5, 3) Q: (0, 4) R: (4, 2) S: (2, -3) T: (-4, -3) DILATION ON GRAPHS: EXAMPLE 2

12 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) DILATION ON GRAPHS: ANSWERS

13 YOU TRY 1)Dilate by a scale factor of ½ 2)Dilate by a scale factor of 4 3)Dilate by a scale factor of ¾ 4)Dilate by a scale factor of 5 5)Dilate by a scale factor of 3 P (0, 9) Q (6, 9) R(6, 0) S(0, 0)

14 YOU TRY: ANSWERS 1)P’(0, 4.5) Q’(3, 4.5) R’(3, 0) S’(0, 0) 2)P’(0, 36) Q’(24, 36) R’(24, 0) S’(0, 0) 3)P’(0, 6.75) Q’(4.5, 6.75) R’(4.5, 0) S’(0, 0) 4)P’(0, 45) Q’(30, 45) R’(30, 0) S’(0, 0) 5)P’(0, 27) Q’(18, 27) R’(18, 0) S’(0, 0) P (0, 9) Q (6, 9) R(6, 0) S(0, 0)

15 Scale factor = image original FIND THE SCALE FACTOR FROM THE ORIGINAL AND THE DILATION 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’P’ Q’Q’ R’R’

16 Scale factor = image original FIND THE SCALE FACTOR FROM THE ORIGINAL AND THE DILATION 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: P’P’ Q’Q’ R’R’

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


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