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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 468 · 40 questions
TalentJR

How to solve it (Across, up, Pythagoras): Distance: across = difference of the x values, up = difference of the y values; distance = √(across² + up²). Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Quadrants by signs: (+, +) first, (−, +) second, (−, −) third, (+, −) fourth.

NameDateTime takenScore ___ / 40
  1. 1.In which quadrant does the point (−2, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  2. 2.What is the midpoint of the line joining (1, 18) and (3, 6)? (a) (1, 6) (b) (4, 24) (c) (2, 12) (d) (12, 2)
  3. 3.What is the midpoint of the line joining (1, 20) and (9, 10)? (a) (4, 5) (b) (15, 5) (c) (10, 30) (d) (5, 15)
  4. 4.What is the distance between the points (2, 6) and (5, 2)? (a) 7 (b) 25 (c) 6 (d) 5
  5. 5.What is the distance between the points (6, 9) and (30, 16)? (a) 25 (b) 625 (c) 31 (d) 26
  6. 6.What is the distance between the points (1, 13) and (9, 7)? (a) 11 (b) 10 (c) 14 (d) 100
  7. 7.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  8. 8.What is the distance between the points (5, 4) and (13, 19)? (a) 18 (b) 23 (c) 289 (d) 17
  9. 9.What is the distance between the points (8, 14) and (23, 6)? (a) 18 (b) 23 (c) 289 (d) 17
  10. 10.What is the distance between the points (0, 7) and (3, 11)? (a) 7 (b) 5 (c) 6 (d) 25
  11. 11.What is the midpoint of the line joining (1, 4) and (11, 8)? (a) (12, 12) (b) (7, 6) (c) (5, 2) (d) (6, 6)
  12. 12.What is the distance between the points (9, 16) and (25, 4)? (a) 20 (b) 400 (c) 28 (d) 21
  13. 13.In which quadrant does the point (2, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  14. 14.What is the distance between the points (5, 6) and (13, 21)? (a) 23 (b) 289 (c) 18 (d) 17
  15. 15.In which quadrant does the point (7, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  16. 16.What is the distance between the points (2, 4) and (11, 16)? (a) 16 (b) 21 (c) 15 (d) 225
  17. 17.What is the midpoint of the line joining (6, 7) and (14, 3)? (a) (5, 10) (b) (4, 2) (c) (20, 10) (d) (10, 5)
  18. 18.What is the distance between the points (4, 20) and (9, 8)? (a) 169 (b) 17 (c) 13 (d) 14
  19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  20. 20.What is the midpoint of the line joining (1, 5) and (5, 1)? (a) (3, 3) (b) (4, 3) (c) (6, 6) (d) (2, 2)
  21. 21.What is the distance between the points (5, 14) and (17, 5)? (a) 225 (b) 16 (c) 21 (d) 15
  22. 22.What is the distance between the points (0, 24) and (12, 8)? (a) 20 (b) 21 (c) 400 (d) 28
  23. 23.What is the distance between the points (5, 0) and (20, 8)? (a) 17 (b) 23 (c) 18 (d) 289
  24. 24.In which quadrant does the point (8, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  25. 25.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  26. 26.What is the distance between the points (4, 6) and (19, 14)? (a) 23 (b) 289 (c) 18 (d) 17
  27. 27.What is the midpoint of the line joining (2, 1) and (12, 11)? (a) (6, 7) (b) (5, 5) (c) (14, 12) (d) (7, 6)
  28. 28.What is the midpoint of the line joining (10, 14) and (20, 8)? (a) (11, 15) (b) (30, 22) (c) (5, 3) (d) (15, 11)
  29. 29.What is the midpoint of the line joining (4, 5) and (10, 15)? (a) (10, 7) (b) (14, 20) (c) (7, 10) (d) (3, 5)
  30. 30.What is the distance between the points (4, 11) and (28, 4)? (a) 26 (b) 625 (c) 31 (d) 25
  31. 31.What is the distance between the points (1, 0) and (9, 6)? (a) 14 (b) 100 (c) 11 (d) 10
  32. 32.In which quadrant does the point (−6, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  33. 33.What is the midpoint of the line joining (8, 14) and (12, 4)? (a) (20, 18) (b) (9, 10) (c) (10, 9) (d) (2, 5)
  34. 34.What is the distance between the points (1, 20) and (17, 8)? (a) 400 (b) 20 (c) 21 (d) 28
  35. 35.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  36. 36.What is the midpoint of the line joining (5, 10) and (9, 6)? (a) (14, 16) (b) (7, 8) (c) (2, 2) (d) (8, 7)
  37. 37.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  38. 38.What is the distance between the points (2, 6) and (7, 18)? (a) 17 (b) 169 (c) 14 (d) 13
  39. 39.What is the midpoint of the line joining (8, 5) and (14, 15)? (a) (10, 11) (b) (11, 10) (c) (3, 5) (d) (22, 20)
  40. 40.In which quadrant does the point (9, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant

Answer key

  1. Third quadrant
  2. (2, 12)
  3. (5, 15)
  4. 5
  5. 25
  6. 10
  7. 17
  8. 17
  9. 17
  10. 5
  11. (6, 6)
  12. 20
  13. First quadrant
  14. 17
  15. Fourth quadrant
  16. 15
  17. (10, 5)
  18. 13
  19. 20
  20. (3, 3)
  21. 15
  22. 20
  23. 17
  24. Fourth quadrant
  25. 10
  26. 17
  27. (7, 6)
  28. (15, 11)
  29. (7, 10)
  30. 25
  31. 10
  32. Third quadrant
  33. (10, 9)
  34. 20
  35. 15
  36. (7, 8)
  37. 25
  38. 13
  39. (11, 10)
  40. First quadrant

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