Unit 1 Packet Honors Math 2 1

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Unit 1 Packet Honors Math 2 1 Day 1 Homework Part 1 Graph the image of the figure using the transformation given and write the algebraic rule. translation: < 1, -2 > translation: < 0, 3 >

Unit 1 Packet Honors Math 2 2 Find the coordinates of the vertices of each figure after the given transformation and write the algebraic rule. 7) Translation: 2 units left and 1 unit down 8) Translation: 2 units down Q(0, -1), D(-2, 2), V(2, 4), J(3, 0) D(-4, 1), A(-2, 5), S(-1, 4), N(-1, 2) 9) Translation: < -4, 4 > 10) Translation: 3 units right and 4 units up J(-1, -2), A(-1, 0), N(3, -3) Z(-4, -3), I(-2, -2), V(-2, -4) Write a specific description of each transformation and give the algebraic rule.

Unit 1 Packet Honors Math 2 3 Day 1 Homework Part 2: Geometry Review 1. In the segment below, another name for AB is 2. Using the segment below, the notation AC means 3. Segment Addition Postulate: In the segment below, AB = 2x + 9, BC = 4x 7, AC = 38 What does x equal? x = 4. Definition of a Midpoint: In the segment below, B is the midpoint of AC. AB = 4x + 2, BC = 6x - 8 What do x and AC equal? x = AC = 5. Classify the following angles: 6. Angle Addition Postulate: 7. Definition of an Angle Bisector: m 1 7x 2 m 2 5x 5 m ABC 75 What is x equal to? x SIDE NOTE: m 1 is the shortcut way of writing the measure of angle 1. It s like math texting you write LOL instead of laughing out loud, math people write m 1 instead of the measure of angle 1. BD bisects ABC m 1 5x 12 m 2 2x 21 What is x and m ABC? x m ABC 8. Congruent ( ) means the same size and shape. Equal ( = ) refers to numerical values. Fill in the following blanks with or =. Use the diagrams at the right to assist you. a. 4 + 6 10 b. Triangle ZYX Triangle WVU Note: this is typically written ZYX WVU Z Y X W V U c. 4x + 8 4(x + 2) d. AB CD e. AB CD 5 5 5 A B C D

Unit 1 Packet Honors Math 2 4 9. Given what you know about right angles and straight angles, solve for the variables: 10. The angles around parallel lines have some really interesting properties can you figure them out? Find the values of a, b, c, and d. Side Note: The little arrows on the two lines are a Geometry notation for saying these lines are parallel. 11. Solve for the missing variables. If U is between T and B, find the value of x and the lengths of the segments. (Hint: Draw a picture for each problem with the given information and then write the equation to solve.) 12. TU = 2x, UB = 3x + 1, TB = 21 13. TU = 4x-1, UB = 2x -1, TB = 5x x = TU = UB = x = TU = UB = TB =

Unit 1 Packet Honors Math 2 5 For 14-15, suppose RS is congruent to MN. For each set, solve for x, and find the length of each segment. 14. RS = 3x + 17, MN = 7x 15 15. RS = x + 10, MN = 2x + 4 x = RS = MN = x = RS = MN = For 16-17, let AB BC. 2x - 8 x + 17 16. x = AB = A B C BC = AC = 17. x + 6 3x - 31 A B C x = AB = BC = AC = 18. m SOX = 160 m 1 = x + 1 m 2 = 3x 1 Find m 2 S O W 1 2 X 19. m BEA = 71. Find m REA. 20. m WOV = 12x. Find m LOV. O B 76 (5x + 1) E 2x (5x + 8) R W L V A

Unit 1 Packet Honors Math 2 6 Day 2 Homework Part 1 Graph the image using the transformation given and give the algebraic rule as requested.

Unit 1 Packet Honors Math 2 7 Find the coordinates of the vertices of each figure after the given transformation and give the algebraic rule, as requested. (Hint: Using graph paper may help on these!) 7) Reflection across the x-axis 8) Reflection across y = -1 K(1, -1), N(4, 0), Q(4, -4) R(-3, -5), N(-4, 0), V(-2, -1), E(0, -4) 9) Reflection across x = 3 10) Reflection across x = -1 F(2, 2), W(2, 5), K(3, 2) V(-3, -1), Z(-3, 2), G(-1, 3), M(1, 1) Write a description of each transformation and give the algebraic rule, as requested.

Unit 1 Packet Honors Math 2 8 Day 3 Homework Part 1 Graph the image of the figure using the transformation given. Also, give the coordinates of the image and the algebraic rule for the transformation.

Unit 1 Packet Honors Math 2 9 Identify the coordinates of the vertices for each figure after the given transformation. Also, give the algebraic rule for each transformation. Use proper notation. 7) rotation 180 about the origin 8) rotation 180 about the origin Z(-1, -5), K(-1, 0), C(1, 1), N(3, -2) L(1, 3), Z(5, 5), F(4, 2) 9) rotation 90 clockwise about the origin 10) rotation 180 about the origin S(1, -4), W(1, 0), J(3, -4) V(-5, -3), A(-3, 1), G(0, -3) Write a description of each transformation AND give the algebraic rule.

Unit 1 Packet Honors Math 2 10 Day 4 Homework Part 1 1. Describe the transformation given by rule x, y 3 x, y. Is it an Isometry"? Why or why not? 2. Write an algebraic rule that would cause dilation by a factor of 3 and dilation by a factor of 1/2. 3. Find the scale factor of the dilation that maps ABCD to A B C D. 4. Find the scale factor of the dilation that maps ABC to A B C. 5. Graph the dilation of the object shown using a scale factor of 2. 6. Graph the dilation of the object shown using a scale factor of ½. Advanced: 7. The package for a model airplane states the scale is 1:63. The length of the model is 7.6 cm. What is the length of the actual airplane? 8. Another model airplane states the scale is 1:96. The length of the real airplane is 48 feet. What is the length of the model?

Unit 1 Packet Honors Math 2 11 Algebra Review: Systems of Equations Read the following example problem about solving by the Substitution Method. Example 1: y = 5 2x 5x 6y = 21 Solution: 1) 5x 6(5 2x) = 21 2) 5x 30 + 12x = 21 Steps explained here: 1) Substitute 5 2x for y in the 2 nd equation. 2) Distribute. 3) 17x 30 = 21 3) Simplify. 4) x = 3 4) Solve by isolating x. 5) y = 5 2(3) = -1 5) Substitute 3 for x in the first equation. The solution is x = 3, y = -1 or (3, -1) Solve each system of equations by the Substitution Method. Show ALL work! Use separate paper if needed. 1. y = 3x 2. y = 2x + 5 5x + y = 24 3x y = 4 3. x = 8 + 3y 2x 5y = 8 4. 3x + 2y = 71 y = 4 + 2x 5. 4x 5y = 92 x = 7y 6. y = 3x + 8 x = y 7. 8x + 3y = 26 2x = y 4 8. x 7y = 13 3x 5y = 23 9. 3x + y = 19 2x 5y = -10 Read the following example problem about solving by the Elimination Method. Example 2: 3x y = 13 8x + 2y = 44 Solution: Steps explained here: 1) 6x 2y = 26 1) Multiply the 1 st equation by 2 to get the same 8x + 2y = 44 number and opposite signs on 1 variable. 2) 14x = 70 2) Add the two equations together. 3) x = 5 3) Solve for x. 4) 3(5) y = 13 4) Substitute 5 for x in the first equation. The solution is x = 5, y = 2 or (5, 2) Solve each system by Elimination. Show ALL work! Use separate paper if needed. 10. 5x y = 20 3x + y = 12 11. x + 3y = 7 x + 2y = 4 12. 3x 2y = 11 3x y = 7

Unit 1 Packet Honors Math 2 12 13. 7x + y = 29 5x + y = 21 14. 8x y = 17 6x + y = 11 15. 9x 2y = 50 6x 2y = 32 16. 7y = 2x + 35 3y = 2x + 15 17. 2y = 3x 1 2y = x + 21 18. 19 = 5x + 2y 1 = 3x 4y 19. u + v = 7 2u + v = 11 20. m n = -9 7m + 2n = 9 21. 3p 5q = 6 2p 4q = 4 22. 4x 5y = 17 3x + 4y = 5 23. 2c + 6d = 14 ½c 3d = 8 24. 3s + 2t = -3 s + 1/3t = -4 Solve each system of equations by using either Substitution or Elimination. 25. r + 4s = -8 3r + 2s = 6 26. 10m 9n = 15 5m 4n = 10 27. 3c 7d = -3 2c + 6d = -34 28. 6g 8h = 50 4g + 6h = 22 29. 2p = 7 + q 6p 3q = 24 30. 3x = -31 + 2y 5x + 6y = 23 31. 3u + 5v = 6 2u 4v = -7 32. 3a 2b = -3 3a + b = 3 33. s + 3t = 27 ½s + 2t = 19

Unit 1 Packet Honors Math 2 13 Algebra Review: Ratios and Proportions Simplify each ratio Ex 1/ 4 to 6 Ex 2/ 3ab:27ab Ex 3/ (4a + 4b) : (a + b) = 4 6 = 2 2 2 3 = 2 3 = 3ab 27ab 3ab = 9 3ab = 1 9 = 4a+4b a+b = 4(a+b) a+b = 4 1 = 4 STEPS 1) Write ratio as a fraction 2) Find and factor out common factors 3) Reduce Simplify each ratio 1) 25 to 15 2) 6 : 9 3) 0.8 to 2.4 4) 36 54 5) 7 14x 6) 12c 14c 7) 2 22x to 35x 8) 0.5ab : 8ab 9) ¼ r 2 to 6r 10) (x 2 + x) to 2x 11) (2x-6) : (6x-4) 12) (9x-9y) to (x-y) Express each ratio in simplest form 13) shorter leg : longer leg 14) hypotenuse to shorter leg 15) shorter leg: hypotenuse 16) hypotenuse: longer leg 17) longer leg to shorter leg 18) longer leg: hypotenuse

Unit 1 Packet Honors Math 2 14 Solve each proportion Ex 1: x 2 = 3 5 STEPS to solve proportions 1) Cross Multiply Ex 2: x + 4 6 = x-4 5 2) Simplify 5x 6 3) Solve for the variable = 5 5 5x+20 =6x-24 6 x= 5 x = 44 Solve each proportion 19) x 3 = 4 5 20) 4 2 = x 5 21) 3x 2 = 7 5 22) 8 2 = x 5 23) x +5 1 = 4 2 24) x +3 4 = 2 3 25) x +2 4 = x +3 5 26) 2x +1 2 = 4x-1 3 27) x +3 2x-1 = 2 3

Unit 1 Packet Honors Math 2 15 Angle Relationships

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