Dilations

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

4 Types of Transformations translations Reflections Rotations Dilations

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

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 12 2 A A’ 16 8 8 4 B C B’ 12 C’ DILATION 6 ORIGINAL

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).

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

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

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

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)

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)

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)

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)

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

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’

Find the scale factor from the original and the dilation P’ 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’

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