1. Transformations:
Translations
Reflections
Rotations
Dilations

2. Reflection
– A transformation resulting from a mirror image or flip over an axis of symmetry. 

3. Reflection
– A transformation resulting from a mirror image or flip over an axis of symmetry. 

4. Reflection
– A transformation resulting from a mirror image or flip over an axis of symmetry. 
Ask students to define constraint. (limitation, restriction)

5. 5 B
A (-4, 1)
B (-2, 4) A C
C (0, 1)
Point C’ needs to be 1 unit away from the x-axis
Point C is 1 unit away from the x-axis
Point B is 4 units away from the x-axis
Point A’ needs to be 1 unit away from the x-axis
Point B’ needs to be 4 units away from the x-axis
Point A is 1 unit away from the x-axis -5 5 A’ C’ B’
Lets reflect over the x-axis.
What do you need to know to reflect the polygon? -5
Notice that orientation has changed; B prime is at the bottom of the polygon.
The axis of symmetry, or sometimes called the line of reflection.
Draw a polygon with three points.

6. A (-4, 3) B (-2, 4) C (0, 3) Lets reflect over the line y = 15 B A C
A (-4, 3)
Point A’ needs to be 2 units away from the line y=1
Point A is 2 units away from the line y = 1
Point B is 3 units away from the line y = 1
Point B’ needs to be 3 units away from the line y = 1
Point C is 2 units away from the line y = 1
Point C’ needs to be 2 units away from the line y = 1
B (-2, 4)
C (0, 3) -5 5 A’ C’ B’ -5
Lets reflect over the line y = 1
The axis of symmetry changes to ….
Using the polygon with these three points…..

7. A (-4, 3) B (-2, 4) C (0, 3) Lets reflect over the y axis5 B B’ A C C’ A’
A (-4, 3)
B (-2, 4)
Point C’ needs to be on the line of symmetry
Point B is 2 units away from the y-axis
Point A’ needs to be 4 units away from the y-axis
Point C is on the line of symmetry
Point B’ needs to be 2 units away from the y-axis
Point A is 4 units away from the y axis
C (0, 3) -5 5 -5
Lets reflect over the y axis
The axis of symmetry changes to ….
Using the polygon with the same three points…..

8. A (-3, 1) B (-2, 4) C (-2, 1) Lets reflect over the y axis5 B B’
Point C is 1 unit away from the y axis
Point A’ needs to be 3 units away from the y-axis
Point A is 3 units away from the y axis
Point C’ needs to be 1 unit away from the y-axis
Point B’ needs to be 2 units away from the y-axis
Point B is 2 units away from the y-axis
A (-3, 1) C’ C
B (-2, 4) A A’
C (-2, 1) -5 5 -5
Lets reflect over the y axis
The axis of symmetry is ….
Let’s look at a different polygon

9. (x,y) becomes (y,x) A (-2, 1) B (-1, 5) C (-4, 4) A’ (1, -2)
Point C’ needs to be 8 units away from the axis of symmetry AT A RIGHT ANGLE
Point C is units away from the axis of symmetry
Point B is 6 units away from the axis of symmetry
Point A’ needs to be 3 units away from the axis of symmetry AT A RIGHT ANGLE
Point B’ needs to be 6 units away from the axis of symmetry AT A RIGHT ANGLE
Point A is 3 units away from the axis of symmetry
C (-4, 4) -5 5 B’ A’
A’ (1, -2) C’
B’ (5, -1) -5
The axis of symmetry is ….
Let’s look at a different polygon
C (4, -4)
(x,y) becomes (y,x)
Lets reflect over the line y = x

10. (x,y) becomes (-y,-x) A (2, 1) B (4, 4) C (1, 4) A’ (-1, -2)5 C B
A (2, 1)
B (4, 4) A
C (1, 4) -5 5 C’ A’
A’ (-1, -2) B’
B’ (-4, -4) -5
The axis of symmetry is ….
Let’s look at a different polygon
C (-4, -1)
(x,y) becomes (-y,-x)
Lets reflect over the line y = -x

11. Reflect over the line x = -15 -5 B B’ C’ C A A’ D’ D
Reflect over the line x = -1