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. 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. 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. 5 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? 6 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 7 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 8 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.