Name Per. 1 - PC\|MAC

1 name _____ Per. _____. Vocabulary Transformation: An operation that _____ or _____ a figure in some way to produce a new figure. The three transformations are _____, _____, and _____. Translation: Preimage ( A) vs. Image ( A' ). 1 2. Example 1: Cross out the example that is NOT a translation. Then describe the remaining translations. A. B. C. * Use one matching point to help you find the rule for the translation. THE MATHEMATICAL WAY TO DESCRIBE TRANSLATIONS . Coordinate Notation Ex: left 3 units; up 7 units (x, y) ( x a, y b ) . left/right up/down Example 3: Rewrite the translation mathematically . 1. left 15 units and up 24 units 2 right 8 units and down 4 units.

2 Example 4: Find the coordinates of the image without graphing. 1. Point is translated 5 units to the left and 6 2. What is the image of after the translation units up to form the point . What are the coordinates defined by )? of ? 3. Use the translation to find 4. Use the translation to find what point translates to: what point translates to: 1. Example 5: Graph the translation using the rule given. Then list the coordinates of the image. 1. 5 units right and 3 unit up 2. 3. **Make sure to label your graph!**. (Ex: Z' X' L' ). Z' ( , ). X' ( , ). L' ( , ). Example 6: Describe the transformation using coordinate notation. 1.

3 2. 3. Critical thinking: Partner up and discuss! 1. Is the following a translation? Why or why not? 2. Is the following a translation? Why or why not? G'. C'. D' D'. G'. C'. 2. Reflection: Line of Symmetry: Example 1: How many lins of symmetry does each figure have? Draw all lines of symmetry. 1. 2. 3. 4. 5. 6. 7. 8. Example 2. 1. Triangle GQS is reflected across the ___-axis. 2. The letter W is reflected across the _____ - axis. y W. x W. 3. Reflect point K across the x-axis. 4. Reflect point across the y- 5. Reflect point across the axis. x-axis. Error Analysis 1. On a quiz Charlie reflected the triangle below across the 2.

4 Jenna reflected the triangle below across the x-axis. y-axis, but it was marked wrong. Describe his error. Describe her error. B B' R R'. T T'. O O'. A P A' P'. 3. Example 3: Graph the reflection described. Then list the coordinates of the image. 1. Reflection in the x-axis 2. Reflection in the y -axis 3. Reflection in the y-axis 4. Graph with vertices and (7, 4). Then reflect across the x-axis and graph . Label the coordinates on the side.. Example 4: Describe the transformation 1. 2. 3. 4. Rotation: Center of Rotation: Direction Degree 90 . Clockwise Counterclockwise (a, b). A full rotation is 360 (-b, a) . every 90 rotation one quadrant over 90.

5 Order switches 90 . (a, b) (b, a) (b, -a). (-a, -b).. 180 = two 90 rotations 90 . Example 1: Graph the rotation and list the coordinates of the image. 1. 90 clockwise 2. 180 counterclockwise 3. 90 counterclockwise 4. Find the coordinates of the image of the triangle shown below after a 90 clockwise rotation. Then graph it. 1st : List the coordinates of the preimage Preimage Image 2nd : Use the coordinate rule: (x, y) (____, _____). 3rd : Apply the rule to each vertex. 4th : Graph the image 5. If is rotated 90 counterclockwise about the 6. If is rotated 180 clockwise about the origin, what are the coordinates of '. origin, what are the coordinates of '.

6 5. Example 4: Describing Rotations 2. 3. __. DESCRIBING TRANFORMATIONS (What you need!!!). Translations Reflections Rotations Shapes face the same Points are directly across from Points are on crack . What to look direction, points are in each other, equidistant for corresponding spots What to Coordinate notation Line of reflection Degree write Direction Ex: translation Ex: reflection in the x-axis Ex: rotation 90 counter- (x, y) (x 2, y + 8) clockwise about the origin Example HINT! count the spaces HINT! Fold your paper to help HINT! Count the # of quadrants Hint! horizontally then vertically from you find the reflection line the figure moves across the preimage to the image Example 5: Describe the transformations.

7 (Be specific). 1. 2. 3. 6. 4. 5. 6. Example 6: Word problems 1. If is translated using 2. If is rotated 90 3. If is reflected across the rule counterclockwise about the the y-axis, what are the what are the coordinates origin, what are the coordinates of '? for '? coordinates of '? 7. Integers and Equations Let's review out integer rules! Adding and Subtracting Integers Multiplying and Dividing Integers SUBTRACTION. ADDITION Are the signs the -Change the ( ) to a (+) same? Are the signs -Change the sign of the the same? 2nd #. **TWO STICK RULE**. Yes NO. Yes NO. The answer The answer ADD SUBTRACT is is the #'s the #'s POSITIVE NEGATIVE.

8 The answer has the same sign as the larger #. Example 1: Simplify 1. 2. 3. 4. 5.. 6. 7. 8. 9. 10.. SOLVING EQUATIONS. Solve: Distribute 1. Distribute Combine like terms 2. Combine like terms Addition - Same sign add them - Different sign subtract them Subtraction 3. Get the variable by itself Division - inverse (opposite) operations Example 2: Solve the equation. 1. 2. 3. 4. 5. 5. 8. 7. 8. 9. 10. 11. 12. 9. Algebra Proofs Vocabulary Proof Two-column proof Statement Reason 1. 1. 2. 2. Algebraic Properties of Equality If a = b, then a + c = b + c If a = b, then a c = b c If a = b, then a c = b c If a = b, then a c = b c If ax + bx, then (a + b)x If a(b + c), then ab + ac.

9 Example 1. 1. Given: Statements Reasons Prove: 2. Given: Statements Reasons Prove: 3. Given: Statements Reasons Prove: 10. 4. Given: Statements Reasons Prove: 5. Given: Statements Reasons Prove: 6. Given: Statements Reasons Prove: REVIEW: Describe the transformation 1. 2. 3. 11. Solving Inequalities and Absolute Value Equations SOLVING INEQUALITIES SIMPLE INEQUALITY GRAPHS. Solve the same way you would solve any equation open circle * There is only one extra rule: closed circle When you multiply or divide both sides by a NEGATIVE # you need to FLIP the symbol Example 1: Solve the inequality and graph its solution. 1. 2. 3. 4.

10 5. 6. 12. What was ABSOLUTE VALUE again??? Ex1: | | Ex 2: | | So if | | , solve for x. ABSOLUTE VALUE EQUATIONS. * You can use the fact that the expression in the absolute value symbol can be either_____ or _____ to help you solve your equation. Ex: | | can be either positive or negative, so . and .. Example 1: solve the equations 1. | | 2. | |. 3. | | 4. | |. 5. | | | |. 6. 13. Solving and Absolute Value Inequalities ABSOLUTE VALUE INEQUALITIES. * When solving an inequality you need to _____ the inequality symbol for the negative equation. Ex: | | can be either positive or negative, so . and Flip the symbol ! Example 2: solve the inequalities 1.