1. Unit 1: Transformations
Final Exam Review

2. Topics to Include Types of Transformations Translations Reflections
Rotations
Dilations
Composition of Transformations

3. Translations Translations are SLIDES
You can slide UP, DOWN, LEFT, and RIGHT
Translate this image up 3 and right 5

4. Translations Translation Notation: (x, y)  (x ± #, y ± #)
You can convert translations into translation notation.
For example, Left 4 and Up 6 would be written (x, y)  (x – 4, y + 6)
You try: Write the translation in translation notation:
1. Right 8, Down Left 4

5. Translations You can also translate points without a graph.
For example: A(-7, 2), B(3, 1), C(4, -8).
Translate using (x, y)  (x – 1, y + 5)
Answer: A’(-8, 7), B’(2, 6), C’(3, -3)
You try: Translate B(5, 2), L(0, -3), T(-2, 8) using (x, y)  (x – 3, y – 10)

6. Translations You can also go backwards!
When given the prime points to start, use the OPPOSITE of the rule given to find the original points.
For example: A’(-7, 2), B’(3, 1), C’(4, -8) was translated
using (x, y)  (x + 6, y – 9). Find the original points!
Answer: A(-13, 11), B(-3, 10), C(-2, 1)
You try: Find the original points if M’(-4, 2), A’(7, -1), N’(8, 11) was translated using (x, y)  (x – 4, y + 3)

7. Reflections
Reflections follow specific rules when reflecting over certain lines.
X Axis Reflection – (x, y)  (x , -y) So the Y VALUE CHANGES SIGNS.
Y Axis Reflection – (x, y)  (-x, y) So the X VALUE CHANGES SIGNS.
Y = X Reflection – (x, y)  (y, x) So the NUMBERS FLIP POSITIONS.
You try: Reflect the image over the x axis.

8. Reflections
Since there are rules, you don’t need a graph to find the new points after a reflection.
For Example: Reflect F(-9, 3) and R(4, -4) over the Y axis.
Answer: F’(9, 3), R’(-4, -4)
You try: Reflect T(5, 3) and S(-3, 2) over the line y = x

9. Reflections You can also reflect over lines that are not axes
Horizontal Lines – y = #
Vertical Lines – x = #
You try: Reflect the image over the line x = -1

10. ROtations The main 3 degrees of rotation also have rules to follow:
90° clockwise – (x, y)  (y, -x) So the points FLIP and the X VALUE CHANGES SIGNS
90° counterclockwise – (x, y)  (-y, x) So the points FLIP and the Y VALUE CHANGES SIGNS
180° - (x, y)  (-x, -y) So both points CHANGE SIGNS
You try: Rotate the image 90° counterclockwise

11. ROtations You can also use the rules to rotate without using a graph
For example: A(-4, 2), B(3, 1), C(-5, 6)
Rotate 180°
Answer: A’(4, -2), B’(-3, -1), C’(5, -6)
You try: D(-4, -1), O(3, 2), G(7, -3) Rotate 90° clockwise

12. Dilations
Dilations either make the image bigger or smaller depending on the SCALE FACTOR
If the Scale factor is GREATER THAN 1, then the image will ENLARGE in size.
If the Scale factor is BETWEEN 0 AND 1, then the image will REDUCE in size.
All you need to do is MULTIPLY both the x and y value by the SCALE FACTOR

13. Dilations Example: Dilate W(-8, 2), I(4, 3), G(3, -4) Scale Factor: 3
Answer: W’(-24, 6), I’(12, 9), G’(9, -12)
You try! Dilate M(9, 1), A(-8, 4), P(4, -3) using a scale factor of 5.

14. Compositions of transformations
A composition of transformations is a MIXTURE of transformations on ONE GRAPH
When graphing these, you must graph the first transformation and then complete the 2nd transformation from the NEW IMAGE and not the ORIGINAL image.
Use PRIME and DOUBLE PRIME to mark the points.

15. Compositions of transformations
You try! Complete the composition of transformations.
Reflect over the x axis
Rotate 90° clockwise

16. ALL DONE