Post on 14-Dec-2015
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: