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

dilation

SWBAT

4 Types of Transformations

translations

Reflections

Rotations

Dilations

DILATION: A transformation where the figure and its image are similar.

New Vocabulary: DIlation

OriginalReduced picture of the originalEnlarged

picture of the original

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

A A’

B B’

C C’

816

12

8

6

4

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

Recall: Scale factor > 1 = enlargedScale factor < 1 = reduced

1.Scale factor = 32.Scale factor = 5/23.Scale factor = ½4.Scale factor = 3/25.Scale factor = 96.Scale factor = 1/8

WILL IT BE ENLARGED OR

REDUCED?

Recall: Scale factor > 1 = enlargedScale factor < 1 = reduced

1.Scale factor = 3 Enlarged2.Scale factor = 5/2 Enlarged3.Scale factor = ½ Reduced4.Scale factor = 3/2 Enlarged5.Scale factor = 9 Enlarged6.Scale factor = 1/8 Reduced

WILL IT BE ENLARGED OR

REDUCED?

Scale factor: corresponding side of dilation (new figure)

corresponding side of original figure (old figure)

Step 1: List all the coordinates of a figureStep 2: Multiply ALL coordinates of the original by the scale factor to get the dilation

Finding a Dilation

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

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

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

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 3P (0, 9) Q (6, 9) R(6, 0)

S(0, 0)

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)

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’

Q’

R’

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’

Q’

R’

Please try the classwork with your table groups

YOU TRY: