Unit 1: Transformations Final Exam Review

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

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

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 2 2. Left 4

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)

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)

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.

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

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

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

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

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

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.

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.

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

ALL DONE