Foundations of Math 2 Final Exam Review Name: ______

UNIT 7: TRANSFORMATIONS

Part 1: Translations

Translations are ______

You can slide ______, ______, ______, and ______

Translate this image up 3 and right 5

Translation Notation: (x, y) ______

You can convert translations into translation notation.

For example, Left 4 and Up 6 would be written (x, y) ______

You try: Write the translation in translation notation:

1. Right 8, Down 22. Left 4

______

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: ______

You try: Translate B(5, 2), L(0, -3), T(-2, 8) using (x, y)  (x – 3, y – 10)

Answer: ______

You can also go backwards!

When given the prime points to start, use the ______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: ______

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)

Answer: ______

Part 2: Reflections

Reflections follow specific rules when reflecting over certain lines.

X Axis Reflection – (x, y) (x , -y) So the ______.

Y Axis Reflection – (x, y) (-x, y) So the ______.

Y = X Reflection – (x, y) (y, x) So the ______.

You try: Reflect the image over the x axis.

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 = xAnswer: ______

You can also reflect over lines that are not axes

Horizontal Lines – ______

Vertical Lines – ______

You try: Reflect the image over the line x = -1

Part 3: Rotations

The main 3 degrees of rotation also have rules to follow:

90° clockwise – (x, y)  (y, -x) So the points ______and the ______

90° counterclockwise – (x, y)  (-y, x) So the points ______and the ______

180° - (x, y)  (-x, -y) So both points ______

You try: Rotate the image 90° counterclockwise

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: ______

You try: D(-4, -1), O(3, 2), G(7, -3) Rotate 90° clockwiseAnswer: ______

Part 4: Dilations

Dilations either make the image bigger or smaller depending on the ______

If the Scale factor is ______, then the image will ______in size.

All you need to do is ______both the x and y value by the ______

Example: Dilate W(-8, 2), I(4, 3), G(3, -4), Scale Factor: 3

Answer: ______

You try! Dilate M(9, 1), A(-8, 4), P(4, -3) using a scale factor of 5. Answer: ______

Part 5: Compositions of Transformations

A composition of transformations is a ______of transformations on ______

When graphing these, you must graph the first transformation and then complete the 2nd transformation from the ______and not the ______image.

Use ______and ______to mark the points.

You try! Complete the composition of transformations.

Reflect over the x axis

Rotate 90° clockwise

‘ ______

“ ______

Unit 7: Page 1 of 3