1. Videos & Songs!
- Colin Dodds song
- transformation style

2. Translations, Reflections, Rotations
RANS ORMATIONS
Translations, Reflections, Rotations

3. TRANSFORMATION Movement of a geometric figure
The result of a transformation is called the prime (’)
Blue figure is “Optimus”
Transformation of “Optimus” is red figure, called “OPTIMUS PRIME”!
Written as Optimus’

4. TRANSLATION
(Slide) - formed by moving every point on a figure the same distance in the same direction

5. HOW TO PERFORM A TRANSLATION
Move the figure 10 units right.
A (-8, 6)  ( , 6)  A’ (2, 6)
B (-3, 6)  ( , 6)  B’ (7, 6)
C (-8, 3)  ( , 3)  C’ (2, 3)
D (-3, 3)  ( , 3)  D’ (7, 3) x y
A (-8, 6)
B (-3, 6)
D (-3, 3)
C (-8, 3)
A’ (2, 6)
B’ (7, 6)
C’ (2, 3)
D’ (7, 3)

6. HOW TO PERFORM A TRANSLATION
To move a units right:
Take each point on the figure, and slide it a units to the right
Algebraically:
Add a to the x-coordinate of each point.
(x, y)  (x + a, y) x y
A (-8, 6)
B (-3, 6)
D (-3, 3)
C (-8, 3)

7. HOW TO PERFORM A TRANSLATION
To move b units left:
Subtract b from the x-coordinate of each point.
(x, y)  (x - b, y)
To move c units up:
Add c to the y-coordinate of each point.
(x, y)  (x, y + c)
To move d units down:
Subtract d from the y-coordinate of each point.
(x, y)  (x, y - d)

8. REFLECTIONS
(Mirror Image/Flip) - a figure is flipped over a line called the line of reflection.

9. HOW TO PERFORM A REFLECTIONx y
B’ (-7, 9)
B (7, 9)
A (3, 6)
C (9, 2)
Reflect the figure over the y-axis
A (3, 6)  A’ (-3, 6)
B (7, 9)  B’ (-7, 9)
C (9, 2)  C’ (-9, 2)
A‘ (-3, 6)
C’ (-9, 2)

10. HOW TO PERFORM A REFLECTION
To reflect over the y-axis:
Move each point of the figure to the opposite side of the axis, the same distance from the axis as the original point.
Algebraically:
Multiply x-coordinate by -1
(x, y)  (-x, y) x y
B (7, 9)
A (3, 6)
C (9, 2)

11. HOW TO PERFORM A REFLECTIONx y
B (7, 9)
A (3, 6)
C (9, 2)
To reflect over the x-axis:
Multiply y-coordinate by -1
(x, y)  (x, -y)
A (3, 6)  A’ (3, -6)
B (7, 9)  B’ (7, -9)
C (9, 2)  C’ (9, -2)
A’ (3, -6)
C’ (9, -2)
B’ (7, -9)

12. REMINDERS FOR REFLECTIONS
When reflecting over the y-axis, image is flipped horizontally.
Change the x-coordinate.
When reflecting over the x-axis, image is flipped vertically.
Change the y-coordinate

13. ROTATIONS
(Turn) – a figure is turned about a point.

14. HOW TO PERFORM A ROTATION
Rotate a figure 90° clockwise about the origin:
SWITCH the coordinates of each point
(x, y)  (y, x)
Then, MULTIPY the NEW second coordinate by -1
(y, x)  (y, -1x)
In the end… (x, y)  (y, -1x) x y
A (8, 9)
B (3, 3)
C (8, 3)

15. HOW TO PERFORM A ROTATION

16. HOW TO PERFORM A ROTATION
Rotate the figure 90°clockwise about the origin
A (-8, 9)  (9, -8)  A’ (9, 8)
B (-3, 3)  (3, -3)  B’ (3, 3)
C (-8, 3)  (3, -8)  C’ (3, 8) x y
A (-8, 9)
B (-3, 3)
C (-8, 3)
C’ (3, 8)
A’ (9, 8)
B’ (3, 3)