Analytic Geometry

Home , Perpendicular

Analytic Geometry

Distance Formula: CLASSWORK

1. Find the distance between (-9, 1) & (-5, -2)

2. Find the distance between (10, 3) & (1, -3)

3. Length of 퐵퐷̅̅̅̅ = ?

4. Length of 퐴퐷̅̅̅̅ = ? #3 - 5

5. Length of 퐷퐶̅̅̅̅ = ?

Distance Formula: HOMEWORK

6. Find the distance between (2, 9) & (-3, 14)

7. Find the distance between (-3, 2) & (9, 7)

8. length of 퐴퐷̅̅̅̅ = ?

9. length of 퐵퐷̅̅̅̅ = ?

#8 - 10 10. length of 퐶퐷̅̅̅̅ = ?

Geometry – Analytic Geometry ~1~ NJCTL.org

Midpoint Formula: CLASSWORK

Calculate the coordinates of the midpoint of the given segments 11. (0, 0), (6, 10) 14. (-3, 8), (13, -6)

12. (2, 3), (6, 7) 15. (-1, -14), (-2, -6)

13. (4, -1), (-2, 5) 16. (3, 2), (6, 6)

17. (-5, 2), (0, 4)

Calculate the coordinates of the other endpoint of the segment with the given endpoint and midpoint M 18. endpoint: (4,6), midpoint: (7,11) 19. endpoint: (2, 6), midpoint: 20. endpoint: (3, -12), midpoint (2,- (-1, 1) 1)

Midpoint Formula: HOMEWORK

Calculate the coordinates of the midpoint of the given segments 21. (0, 0), (8, 4) 24. (6, 0), (2, 7)

22. (-1, 3), (7, -1) 25. (-5, -3), (-3, -5)

23. (3, 5), (7, -9) 26. (13, 8), (-6, -6)

27. (-4, -2), (1, 3)

Calculate the coordinates of the other endpoint of the segment with the given endpoint and midpoint M 28. endpoint: (-5, 9) 29. endpoint: (6, 7) 30. endpoint: (2, 4) midpoint (-8, -2) midpoint (10, -7) midpoint (-1, 7)

Geometry – Analytic Geometry ~2~ NJCTL.org

Partitions of a Line Segment: CLASSWORK PARCC-type Questions: 31. Line segment AB in the coordinate plane has endpoints with coordinates A (3, -10) and B(-6, -1). a) Graph 퐴퐵̅̅̅̅

b) Find 2 possible locations for point C so that C divides 퐴퐵̅̅̅̅ into 2 parts with lengths in a ratio of 1:2.

32. Line segment EF in the coordinate plane has endpoints with coordinates E (-10, 11) and F (5, -9). a) Graph 퐸퐹̅̅̅̅

b) Find 2 possible locations for point G so that G divides 퐸퐹̅̅̅̅ into 2 parts with lengths in a ratio of 2:3.

33. Line segment JK in the coordinate plane has endpoints with coordinates J (11, 11) and K (-10, -10). Find two possible locations for point P that divides 퐽퐾̅̅̅ into two parts with lengths in a ratio of 3:4.

34. Line segment LM in the coordinate plane has endpoints with coordinates L (-12, 10) and M (6, -8). Find two possible locations for point P that divides 퐿푀̅̅̅̅ into two parts with lengths in a ratio of 2:7.

35. Line segment RS in the coordinate plane has endpoints with coordinates R(7, -11) and S(-9, 13). Find two possible locations for point P that divides 푅푆̅̅̅̅ into two parts with lengths in a ratio of 3:5.

Partitions of a Line Segment: HOMEWORK PARCC-type Questions: 36. Line segment AB in the coordinate plane has endpoints with coordinates A (5, -7) and B(-10, 3). a) Graph 퐴퐵̅̅̅̅

b) Find 2 possible locations for point C so that C divides 퐴퐵̅̅̅̅ into 2 parts with lengths in a ratio of 1:4.

37. Line segment EF in the coordinate plane has endpoints with coordinates E (-10, 11) and F (10, -9). a) Graph 퐸퐹̅̅̅̅

b) Find 2 possible locations for point G so that G divides 퐸퐹̅̅̅̅ into 2 parts with lengths in a ratio of 7:3.

38. Line segment JK in the coordinate plane has endpoints with coordinates J (11, 11) and K (-10, -10). Find two possible locations for point P that divides 퐽퐾̅̅̅ into two parts with lengths in a ratio of 2:5.

39. Line segment LM in the coordinate plane has endpoints with coordinates L (-12, 10) and M (6, -8). Find two possible locations for point P that divides 퐿푀̅̅̅̅ into two parts with lengths in a ratio of 5:4.

40. Line segment RS in the coordinate plane has endpoints with coordinates R(7, -11) and S(-9, 13). Find two possible locations for point P that divides 푅푆̅̅̅̅ into two parts with lengths in a ratio of 1:7.

Slopes of Parallel & Perpendicular Lines: CLASSWORK Identify the slope of the line containing the given points: 41. (-2,11), (-5, 2) 42. (-4,11), (-4, -7) 43. (-2,22), (-5, 22) 44. Is the following system of equations parallel? Justify your answer. A B

45. Is the following system of equations perpendicular? Justify your answer. A B

46. If one line has a slope of -5, what must be the slope of a line parallel to it?

47. If one line passes through the points (-1, 2) & (7, 6), what must be the slope of a line parallel to it?

48. If one line passes through the points (3, -5) & (1, 9) and a parallel line passes through the point (3, 4), what is the other point that would lie on the 2nd line?

49. If one line has a slope of ½, what must be the slope of a line perpendicular to it?

50. If one line passes through the points (3, -5) & (1, 9), what must be the slope of a line perpendicular to it?

51. If one line passes through the points (5, 2) & (7, 6) and a perpendicular line passes through the point (3, 4), what is the other point that would lie on the 2nd line?

Slopes of Parallel & Perpendicular Lines: HOMEWORK Identify the slope of the line containing the given points: 52. (-6,12), (-2, 5) 53. (14,11), (-14, 11) 54. (-2,17), (-2, 18) 55. Is the following system of equations parallel? Justify your answer. A B

56. Is the following system of equations perpendicular? Justify your answer. A B

57. If one line has a slope of ½, what must be the slope of a line parallel to it?

58. If one line passes through the points (3, -5) & (1, 9), what must be the slope of a line parallel to it?

59. If one line passes through the points (5, 2) & (7, 6) and a parallel line passes through the point (3, 4), what is another point that would lie on the 2nd line?

60. If one line has a slope of -5, what must be the slope of a line perpendicular to it?

61. If one line passes through the points (-1, 2) & (7, 6), what must be the slope of a line perpendicular to it?

62. If one line passes through the points (3, -5) & (1, 9) and a perpendicular line passes through the point (3, 4), what is another point that would lie on the 2nd line?

Equations of Parallel & Perpendicular Lines: CLASSWORK 63. Find an equation of the line in point-slope form passing through point (-2, 5) and parallel to the line whose equation is 4x – 2y = -5

64. Two lines are represented by equations: 2x + 4y = 21 and y = kx – 12. What value of k will make lines parallel?

65. Find an equation of the line in slope-intercept form passing through point (-4,6) and parallel to the line whose equation is y = -¾ x + 11

66. The sides of a quadrilateral lie on the lines y = 4x + 5, y = 1/3x +7, 8x – 2y = 1, and x – 3y = 2. Is the quadrilateral a parallelogram? Justify your answer.

67. Find an equation of the line passing through point (4, -5) and perpendicular to the line whose equation is 3x – 6y = -11.

68. Two lines are represented by equations: -3x + 6y =21 and y = kx +5. What value of k will make lines perpendicular?

69. Find an equation of the line passing through point (8, -2) and perpendicular to the line whose equation is y = 4x + 11.

70. The sides of a quadrilateral lie on the lines y= 4x + 5, y = 1/3x + 7, x + 4y = 1, and x – 3y = 2, is the quadrilateral a rectangle? Justify your answer.

71. Determine if the following equations are parallel, perpendicular, or neither. Justify your answer. 4x + 3y = 9 6x – 8y = 20

72. Determine if the following equations are parallel, perpendicular, or neither. Justify your answer. 5(x + 3) = 3y + 12 5x + 3y = 15

Equations of Parallel & Perpendicular Lines: HOMEWORK 73. Find an equation of the line in point-slope form passing through point (-3, 2) and parallel to the line whose equation is 6x – 2y = 7.

74. Two lines are represented by equations: -4x + 12y = 21 and y = kx – 12. What value of k will make lines parallel?

75. Find an equation of the line in point-slope form passing through point (-8,3) and parallel to the line whose equation is y = -¾ x + 11.

76. The sides of a quadrilateral lie on the lines 3x + y = 7, x + y = 12, 6x – 2y = 2, and x – y = 2. Is the quadrilateral a parallelogram? Justify your answer.

77. Find an equation of the line passing through point (-6,2) and perpendicular to the line whose equation is 4x + 6y = -1

78. Two lines are represented by equations: 10x – 15y = 21 and y = kx + 5. What value of k will make lines perpendicular?

79. Find an equation of the line passing through point (8,-2) and perpendicular to the line whose equation is y = -2x + 11

80. The sides of a quadrilateral lie on the lines 4x – y = 5, x + 4y = 7, 8x – 2y = 1, and 3x + 12y = 2. Is the quadrilateral a rectangle? Justify your answer.

81. Determine if the following equations are parallel, perpendicular, or neither. Justify your answer. 9x + 5y = 32 4.5x + 2.5y = 7.5

82. Determine if the following equations are parallel, perpendicular, or neither. Justify your answer. 7(x – 1) = 3y + 21 3.5x + 1.5y = 4.5

Triangle Coordinate Proofs: CLASSWORK – CP For numbers 83 – 84 find (a.) the length of AB and (b.) the midpoint coordinates of . 83. A(6, 7), B(4, 3) 84. A(1, 5), B(2, 3)

85. If one line has a slope of -3 what must be the slope of (a.) any line parallel to it and (b.) any line perpendicular to it?

86. If one line passes through the points (0,3) and (-4,1) what must be the slope of (a.) any line parallel to that first line and (b.) any line perpendicular to that first line?

Statements Reasons 87. Given: 퐺퐽⃗⃗⃗⃗ 푏푖푠푒푐푡푠 ∠푂퐺퐻 1. 퐺퐽⃗⃗⃗⃗ bisects OGH 1. Prove: ∆퐺퐽푂 ≅ ∆퐺퐽퐻 2. 2. Definition of an

angle bisector

3. 퐺퐽̅̅̅ ≅ 퐺퐽̅̅̅ 3.

4. 푂퐺 = ______, 4. Distance Formula

퐻퐺 = ______

5. ̅̅̅̅ ̅̅̅̅ 5. 푂퐺 ≅ 퐻퐺

  6. 6. GJO GJH

 Statements Reasons 88.  Given: Coordinates of the vertices of ∆푂푃푀 & ∆푂푁푀 Prove: ∆푂푃푀 & ∆푂푁푀 are congruent 1. Coordinates of 1. isosceles triangles vertices of OPM and ONM 2. OP = ______, 2. Distance Formula PM = ______, MN = ______, NO = ______3. 푂푃̅̅̅̅ ≅ 푃푀̅̅̅̅̅ ≅ 3. 푀푁̅̅̅̅̅ ≅ 푁푂̅̅̅̅ 4. 푂푀̅̅̅̅̅ ≅ 푂푀̅̅̅̅̅ 4. 5. OPM and 5. ONM are isosceles 6. OPM ONM 6.

Triangle Coordinate Proofs: HOMEWORK – CP For numbers 89 – 90 find (a.) the length of AB and (b.) the midpoint coordinates of . 89. A(14, 2), B(7, 8) 90. A(0, 0), B(5, 12)

91. If one line has a slope of 2/7 what must be the slope of (a.) any line parallel to it and (b.) any line perpendicular to it?

92. If one line passes through the points (-2,5) and (7,-1) what must be the slope of (a.) any line parallel to that first line and (b.) any line perpendicular to that first line?

Statements Reasons 93. 1. Given: 푂푆⃗⃗⃗⃗⃗ ⊥ 푅푇̅̅̅̅ 1. Given Prove: 푂푆̅̅̅̅ 푏푖푠푒푐푡푠 ∠푇푂푅 2. RSO and TSO 2. are right angles 3. RSO ≅ TSO 3. 4. 푂푆̅̅̅̅ ≅ 푂푆̅̅̅̅ 4. 5. OR = 6, OT = 6 5. 6. 푂푅̅̅̅̅ ≅ 푂푇̅̅̅̅ 6. 7. SOR  SOT 7.

8. SOR  SOT 8.

⃗⃗⃗⃗⃗ 9. 9. 푂푆 bisects TOR  

⃗⃗⃗⃗⃗ 94. Given:Statements G is the midpoint Reasonsof 퐻퐹 Prove: ∆퐺퐻퐽 ≅ ∆퐺퐹푂 1. 1. Given

2. 2. Vertical Angles are 

3. 퐻퐺̅̅̅̅ ≅ 퐹퐺̅̅̅̅ 3.

G 3. 푂퐺 = ______4. Distance Formula

퐽퐺 = ______

5. 푂퐺̅̅̅̅ ≅ 퐽퐺̅̅̅ 5.

6. 6. ∆퐺퐻퐽 ≅ ∆퐺퐹푂

Triangle Coordinate Proofs: CLASSWORK – Honors For numbers 83 – 84 find (a.) the length of AB and (b.) the midpoint coordinates of . 83. A(6, 7), B(4, 3) 84. A(1, 5), B(2, 3)

85. If one line has a slope of -3 what must be the slope of (a.) any line parallel to it and (b.) any line perpendicular to it?

86. If one line passes through the points (0,3) and (-4,1) what must be the slope of (a.) any line parallel to that first line and (b.) any line perpendicular to that first line?

87. Given: 퐺퐽⃗⃗⃗⃗ 푏푖푠푒푐푡푠 ∠푂퐺퐻 Prove: ∆퐺퐽푂 ≅ ∆퐺퐽퐻

88. Given: Coordinates of the vertices of ∆푂푃푀 & ∆푂푁푀 Prove: ∆푂푃푀 & ∆푂푁푀 are congruent isosceles triangles

Triangle Coordinate Proofs: HOMEWORK – Honors For numbers 89 – 90 find (a.) the length of AB and (b.) the midpoint coordinates of . 89. A(14, 2), B(7, 8) 90. A(0, 0), B(5, 12)

91. If one line has a slope of 2/7 what must be the slope of (a.) any line parallel to it and (b.) any line perpendicular to it?

92. If one line passes through the points (-2,5) and (7,-1) what must be the slope of (a.) any line parallel to that first line and (b.) any line perpendicular to that first line?

93. Given: 푂푆⃗⃗⃗⃗⃗ ⊥ 푅푇̅̅̅̅ Prove: 푂푆̅̅̅̅ 푏푖푠푒푐푡푠 ∠푇푂푅

94. Given: G is the midpoint of 퐻퐹⃗⃗⃗⃗⃗ Prove: ∆퐺퐻퐽 ≅ ∆퐺퐹푂

Equations of a Circle & Completing the Square: CLASSWORK What are the center and the radius of the following circles? 95. (푥 + 2)2 + (푦 − 4)2 = 16 96. (푥 − 3)2 + (푦 − 7)2 = 25 97. (푥)2 + (푦 + 8)2 = 1 98. (푥 − 7)2 + (푦 + 1)2 = 17 99. (푥 + 6)2 + (푦)2 = 32

Write the standard form of the equation for the given information. 100. center (3,2) radius 6 101. center (-4, -7) radius 8 102. center (5, -9) radius 10 103. center (-8, 0) diameter 14 104. center (4,5) and point on the circle (3, -7) 105. diameter with endpoints (6, 4) and (10, -8) 106. center (4, 9) and tangent to the x-axis

PARCC-type Questions: Write the standard form of the equation for the given information. 107. 푥2 + 4푥 + 푦2 − 8푦 = 11 108. 푥2 − 10푥 + 푦2 + 2푦 = 11 109. 푥2 + 7푥 + 푦2 = 11

Are the following points on the circle (x-3)2+(y+4)2=25? Support your answer with your work. 110. (3,1) 111. (0,0) 112. (4,-1)

PARCC-type Question: 113. The equation 푥2 + 푦2 − 6푥 + 10푦 = 푏 describes a circle. a. Determine the x-coordinate of the center of the circle.

b. Determine the y-coordinate of the center of the circle.

c. If the radius of the circle is 8 units, what is the value of b in the equation?

Equations of a Circle & Completing the Square: HOMEWORK What are the center and the radius of the following circles? 114. (푥 − 9)2 + (푦 + 5)2 = 9 115. (푥 + 11)2 + (푦 − 8)2 = 64 116. (푥 + 13)2 + (푦 − 3)2 = 144 117. (푥 − 2)2 + (푦)2 = 19 118. (푥 − 6)2 + (푦 − 15)2 = 40

Write the standard form of the equation for the given information. 119. center (-2, -4) radius 9 120. center (-3, 3) radius 11 121. center (5, 8) radius 12 122. center (0 , 8) diameter 16 123. center (-4,6) and point on the circle (-2, -8) 124. diameter with endpoints (5, 14) and (11, -8) 125. center (4, 9) and tangent to the y-axis

PARCC-type Questions: Write the standard form of the equation for the given information. 126. 푥2 − 2푥 + 푦2 + 10푦 = 11 127. 푥2 + 12푥 + 푦2 + 20푦 = 11 128. 4푥2 + 16푥 + 4푦2 − 8푦 = 12

Are the following points on the circle (x-5)2+(y-12)2=169? Support your answer with your work. 129. (-4,2) 130. (0,0) 131. (-7,7)

PARCC-type Question: 132. The equation 푥2 + 푦2 + 12푥 − 4푦 = 푏 describes a circle. a. Determine the x-coordinate of the center of the circle.

b. Determine the y-coordinate of the center of the circle.

c. If the radius of the circle is 5 units, what is the value of b in the equation?

Analytic Geometry Unit Review

Multiple Choice – Choose the correct answer for each question. No partial credit will be given. 1. What is the distance between points (-2, 1) and (2, 4)? a. 3 b. c. 5 d.

2. What is the distance between points (1, 2) and (3, 4). Circle all that apply. a. 2 b. c. 2 d. 8 e. 2√5 f. 2√13

3. What is the midpoint between points (-1, 4) and (7, 6) a. (6, 5) b. (3, 5) c. (5, 5) d. (5, 3)

4. Find the midpoint between points (7, -9) and (3, 5) a. (5, 2) b. (2, 5) c. (-5, 2) d. (5, -2)

5. The midpoint of a line segment is (3, 4). One endpoint has the coordinates (-3, -2). What are the coordinates of the other endpoint? a. (9, 10) b. (-3, -2) c. (10, 9) d. (1, 0)

6. If one line passes through the points (7, -3) & (-2, 3), what must be the slope of a line parallel to it? 3 a. − 2 2 b. − 3 c. 0 d. undefined

7. If one line passes through the points (-5, 3) & (9, 7) and a perpendicular line passes through the point (-1, -3), what is another point that would lie on the 2nd line? Circle all that apply. a. (-3, 4) b. (-3, -11) c. (6, -1) d. (6, -5) e. (-10, 1) f. (1, 13)

8. What is the equation of the line parallel to 2x + 8y = 10 and passes thru (-1, 5)? a. y – 5 = - ¼(x – 1) b. y – 5 = - ¼(x + 1) c. y – 5 = 4(x – 1) d. y – 5 = 4(x + 1)

9. What is the equation of the line perpendicular to y – 3 = 2/3(x + 3) and has an x-intercept of 6? a. y = 2/3x + 4 b. y = 2/3x – 4 c. y = -3/2x + 6 d. y = -3/2x + 9

10. What is the equation of the circle drawn in the figure to the right? a. (푥 − 6)2 + (푦 − 4)2 = 4 b. (푥 + 6)2 + (푦 + 4)2 = 6 c. (푥 − 6)2 + (푦 − 4)2 = 16 d. (푥 + 6)2 + (푦 + 4)2 = 36

Short Constructed Response – Write the correct answer for each question. 11. a) Write the distance formula and use it to find the distance between point B (-2, 5) to point C (4, -3).

b) What are the coordinates of the midpoint of 퐵퐶̅̅̅̅?

12. The equation of a circle is 푥2 + 푦2 − 8푥 − 6푦 = 75. Write the equation in standard form.

13. Line segment AB in the coordinate plane has endpoints with coordinates A (-11, -6) and B (11, 5). a) Graph 퐴퐵̅̅̅̅ b) Find 2 possible locations for point C so that C divides 퐴퐵̅̅̅̅ into 2 parts with lengths in a ratio of 6:5.

Extended Constructed Response – Solve the problem, showing all work. 14. Draw the line m on the graph provided so that m passes thru (1, 4) and (5, -3) a. What is the equation of the line? b. Construct a parallel line n that contains (3, 7). c. What is the equation of line n? d. Construct a line p that is perpendicular to the original line that contains A(3, 7). e. What is the equation of line p?

Statements Reasons 1. 1. 15. Given: The coordinates of ∆퐺퐻퐽 & ∆퐺퐹푂 2. 2. Vertical Angles Prove: ∆퐺퐻퐽 ≅ ∆퐺퐹푂 are  3. 푚퐻퐽 = ______3. Slope formula 푚푂퐹 = ______4. 퐻퐽̅̅̅̅ || 푂퐹̅̅̅̅ 4. GGGG 5. ∠퐻 ≅ ∠퐹 5. (3, 6. ______is the 6. Midpoint formula midpoint of 퐽푂̅̅̅ 7. 푂퐺̅̅̅̅ ≅ 퐽퐺̅̅̅ 7. 8. ∆퐺퐻퐽 ≅ ∆퐺퐹푂 8.

16. The points (3, 2) and (9, 12) are the endpoints of a diameter of a circle. a. Where is the center of the circle?

b. How long is the diameter of the circle?

c. Write the equation of the circle?

d. Is the point (5, 6) inside, on, or outside the circle? Justify your answer.

17. The equation 푥2 + 푦2 − 8푥 + 6푦 = 푏 describes a circle. a. Determine the x-coordinate of the center of the circle.

b. Determine the y-coordinate of the center of the circle.

c. If the radius of the circle is 10 units, what is the value of b in the equation?

Answers: CW/HW problems:

1. 5 31. See graph below for a) & b) 2. 3 13 ≈ 10.82 3. 34 √34 ≈ 5.83 4. 13 5. 3 2 ≈ 4.24 6. 5 2 ≈ 7.07 7. 13 8. 53 ≈ 7.28 9. 26 ≈ 5.10 10. 10 ≈ 3.16 11. (3, 5) 12. (4, 5) 13. (1, 2) 14. (5, 1) 32. See graph below for a) & b) 15. (-1.5, -10) 16. (4.5, 4) 17. (-2.5, 3) 18. (10, 16) 19. (-4, -4) 20. (1, 10) 21. (4, 2) 22. (3, 1) 23. (5, -2) 24. (4, 3.5) 25. (-4, -4) 26. (3.5, 1) 27. (-1.5, 0.5) 28. (-11, -13) 29. (14, -21) 30. (-4, 10)

33. (-1, -1) & (2, 2) 34. (2, -4) & (-8, 6) 35. (-3, 4) & (1, -2)

36. See graph below for a) & b) 48. Multiple Answers: Sample points that work include (4, -3) & (2, 11) 49. -2 50. 1/7 51. Multiple Answers: Sample points that work include (1, 5) & (5, 3) 52. -7/4 53. 0 54. No slope (Undefined) 55. a. yes; slope of j & k = 4/7; 1 1 b. no; slope of j= - /6, slope of k= - /7 56. a. no slope of j= 3/2; slope of k=-1/2; b. yes, slope of j=1/5; slope of k= -5 57. ½ 58. -7 59. Multiple answers: Sample points that work include (2, 2) & (0, -2) 37. See graph below for a) & b) 60. m = 1/5 61. -2 62. Multiple Answers: Sample points that work include (-4, 3) or (10, 5) 63. y -5= 2(x+2) 64. k= -1/2 65. y= -3/4x+3 66. Yes,푦 = 4푥 + 5䚫8푥 − 2푦 = 1 1 ; 푦 = 푥 + 7䚫푥 − 3푦 = 2 3 67. y=-2x+3 68. k= -2 69. y=-1/4x 70. no, y=4x +5 and y =1/3x +7 are not perpendicular 71. perpendicular 72. neither 73. y -2 = 3(x+3) 38. (-4, -4) & (5, 5) 74. k=1/3 39. (-4, 2) & (-2, 0) 75. y-3=-3/4(x+8) 40. (-7, 10) & (5, -8) 76. no; 41. 3 77. y=3/2x+11 42. No slope (undefined) 78. k=-3/2 43. 0 79. y=1/2x-6 44. a. no; slope of j=2, slope of k = 4/3; 80. yes, slopes are m=-1/4 and 4 b. yes; slope of j and k = -4/5 81. parallel 45. a. yes; slope of j= -1/6; slope of k=6; 82. neither b. no slope of j= -1; slope of k= 1/3 83. a.) 2√5 or 4.5 b.) (5, 5) 46. m = -5 84. a.) √73 or 8.5 b.) (0.5, 1) 47. ½ 85. a.) -3 b.) -1/3

86. a.) ½ b.) -2 6. 푂푅̅̅̅̅ ≅ 푂푇̅̅̅̅ 6. Def. of  87. segments Statements Reasons 7. SOR SOT 7. HL Theorem 1. 퐺퐽⃗⃗⃗⃗ bisects OGH 1. Given 8. SOR  SOT 8. CPCTC 2. OGJ  HGJ 2. Definition of an 9. 푂푆⃗⃗⃗⃗⃗ bisects TOR 9. Definition of an angle bisector angle bisector 3. 퐺퐽̅̅̅ ≅ 퐺퐽̅̅̅ 3. Reflexive Prop. of  94. 4. 푂퐺 = √34, 4. Distance Formula Statements Reasons 1. G is the midpoint 1. Given 퐻퐺 = √34 ̅̅̅̅ 5. 푂퐺̅̅̅̅ ≅ 퐻퐺̅̅̅̅ 5. Def. of  of 퐻퐹 segments 2. HGJ  FGO 2. Vertical Angles 6. GJO  GJH 6. SAS Postulate are  ̅̅̅̅ ̅̅̅̅ 3. 퐻퐺 ≅ 퐹퐺 3. Def. of midpoint 88. 4. 푂퐺 = 3√2 4. Distance Formula  퐽퐺 = 3√2  Statements Reasons 5. 푂퐺̅̅̅̅ ≅ 퐽퐺̅̅̅ 5. Definition of  1. Coordinates of 1. Given segments vertices of OPM 6. GHJ GFO 6. SAS Postulate and ONM 2. OP = 5, PM = 5, 2. Distance Formula 95. C(-2,4); r=4 MN = 5, NO = 5 96. C (3,7); r=5 3. 푂푃̅̅̅̅ ≅ 푃푀̅̅̅̅̅ ≅ 3. Def. of  97. C (),-8); r=1 ̅̅̅̅̅ ̅̅̅̅ 푀푁 ≅ 푁푂 segments 98. C (7,-1); r= √17 4. 푂푀̅̅̅̅̅ ≅ 푂푀̅̅̅̅̅ 4. Reflexive Prop. of 99. C (-6,0); r =4√2  2 2 5. OPM and 5. Definition of an 100. (x-3) + (x-2) =36 2 2 ONM are isosceles isosceles triangle 101. (x+4) + (Y+7) =64 6. OPM ONM 6. SSS Postulate 102. (x-5)2 + (y+9)2 = 100 103. (x+8)2 + y2 =49 89. a.) √85 or 9.2 b.) (10.5, -5) 104. (x-4)2 + (y-5)2 =145 90. a.) 13 b.) (-2.5, 6) 105. (x-8)2 + (y+2)2 =40 91. a.) 2/7 b.) -7/2 106. (x-4)2 + (y-9)2 =81 92. a.) -2/3 b.) 3/2 2 2 93. 107. (x+2) + (y-4) =31 2 2 Statements Reasons 108. (x-5) + (y+1) =37 1. 푂푆̅̅̅̅ ⊥ 푅푇̅̅̅̅ 1. Given 109. (x+3.5)2 + y2 =23.25 2. RSO and TSO 2. Definition of ⊥ 110. yes; (3-3)2+(1+4)2=25 are right angles lines 111. yes; (0-3)2+(0+4)2=25 3. RSO ≅ TSO 3. All right angles 112. no; (4-3)2+(-1+4)2=10 are congruent 113. a) x-coord. = 3 4. 푂푆̅̅̅̅ ≅ 푂푆̅̅̅̅ 4. Reflexive Prop. of b) y-coord. = -5  5. OR = 6, OT = 6 5. Given in diagram; c) b = 30 or Distance formua 114. C (9,-5) r=3

115. C -11, 8) r=8 125. (x-4)2 + ( y-9)2 =130 116. C(-13, 3) r=12 126. (x-1)2 + (y+5)2 =37 117. C(2,0) r= √19 127. (x+6)2 + (y+10)2 =147 2 2 118. C (6,15) r=2√10 128. (x+2) + (y-1) =8 2 2 119. (x+2)2 +(Y+4)2 =81 129. no; (-4-5) +(2-12) =181 2 2 120. (x+3)2 + (y-3)2 =121 130. yes; (0-5) +(0-12) =169 2 2 121. (x-5)2 + (y-8)2 =144 131. yes; (-7-5) +(7-12) =169 122. x2 + (y-8)2 =64 132. a) x-coord. = -6 b) y-coord. = 2 123. (x+4)2 + (y-6)2 =200 c) b = -15 124. (x-8)2 + (y-3)2 = 130

Answers: Unit Review

Multiple Choice Extended Constructed Response 1. C 14. a. y – 4 = -7/4(x – 1) 2. B & C or y + 3 = -7/4(x – 5) 3. B b. construct 푦 − 7 = −7/4(푥 − 3) 4. D in coordinate plane 5. A c. y – 7 = -7/4(x – 3) or 6. B y = -7/4x + 49/4 or 7. A & E 7x + 4y = 49 8. B d. construct 푦 − 7 = 4/7(푥 − 3) 9. D in coordinate plane 10. C e. 푦 − 7 = 4/7(푥 − 3) or y = 4/7x + 37/7 or Short Constructed Response 4x – 7y = -37 11. d = 10; midpoint = (1, 1) 15. 12. (푥 − 4)2 + (푦 − 3)2 = 100 Statements Reasons 13. See graph below for a) & b) 1. The coordinates of 1. Given ∆퐺퐻퐽 & ∆퐺퐹푂 2. HGJ  FGO 2. Vertical Angles are  3. 푚퐻퐽 = 0 3. Slope formula, or 푚푂퐹 = 0 Horizontal lines have a slope of 0. 4. 퐻퐽̅̅̅̅ || 푂퐹̅̅̅̅ 4. Def. of || lines 5. ∠퐻 ≅ ∠퐹 5. Alt. Int. ∠푠 ≅ 6. G is the midpoint 6. Midpoint formula of 퐽푂̅̅̅ 7. 푂퐺̅̅̅̅ ≅ 퐽퐺̅̅̅ 7. Definition of midpoint 8. GHJ  GFO 8 . AAS Theorem

 

16. a. (6,7) b. 11.662 17. Equation: c. (푥 − 6)2+(푦 − 7)2 = 136 (푥 − 4)2 + (푦 + 3)2 = 푏 + 25 d. (5 − 6)2+(6 − 7)2 = 2 a. 4 2 < 136, so the point is inside the b. -3 circle. c. b = 75, since 푟2 = 100