1. Students will be able to dilate shapes
Lesson 2.7
Dilations
Students will be able to dilate shapes

2. Youtube Notes
(notes) (help with page 1 and 2) (help with page 3)

3. Dilations
A dilation is a type of transformation that enlarges or reduces a figure but the shape stays the same.
Pre-image and Image will be similar, but is not congruent.
The dilation is described by a scale factor and a center of dilation.

4. Dilations
The scale factor k is the ratio of the length of any side in the image to the length of its corresponding side in the pre-image. It describes how much the figure is enlarged or reduced.

5. The dilation is an enlargement if the scale factor is greater than 1.
Two types of dilations
Enlargement
Reduction
The dilation is an enlargement if the scale factor is greater than 1.
The dilation is a reduction if the scale factor is between 0 and 1.

6. Enlarge by a scale factor of 2 4, 6
Use Point A: (2, 3) a) (x, y)  (2x, 2y) __________________ New coordínate: ( ) b) (x, y)  ( 1 4 x, 1 4 y)__________________ New coordinate: ( ) c) (x, y)  (2.5x, 2.5y)_____________________ New coordinate: ( ) d) (x, y)  (0.5x, 0.5Y)____________________
Enlarge by a scale factor of 2
4, 6
Reduce by a scale factor of ¼
0.5, 0.75
Enlarge by a scale factor of 2.5
5, 7.5
Reduce by a scale factor of 0.5
1, 1.5

7. Given the vertices of the triangle, find a dilation by a scale factor of 3.x B’ C’
A (1,2)
B (3,3)
C (1,3)
A’ (3,6) A’
B’ (9,9) C B
C’ (3,9) A

8. Given the vertices of the rectangle, find a dilation by a scale factor of 2/3.x
A (-6,-3)
B (-6,3)
C (6,3)
D (6,-3)
A’ (-4,-2)
B’ (-4,2)
C’ (4,2) B C
D’ (4,-2) B’ C’ A’ D’ A D

9. Scale factor of 2 Scale factor of 1/2 Scale factor of 3
DILATION
SHAPE:
A (-2, 0)
B (0, -2)
C (2, 0)
D (2, 4)
Color Red
Scale factor of 2
Scale factor of 1/2
Scale factor of 3
Algebraic Representation
(x, y)  ( )
(x, y)  ( )
(x, y)  ( )
New Coordinates:
A’ ( )
B’ ( )
C’ ( )
D’ ( )
Color Blue
A’’ ( )
B’’ ( )
C’’ ( )
D”( )
Color Green
A’’’ ( )
B’’’ ( )
C’’’ ( )
D’’’ ( )
Color Pink