1. UNIT 7: 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 translation 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 22. 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 ENLARGEin 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 2 nd 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