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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 224 · 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.What is the distance between the points (2, 12) and (18, 0)? (a) 400 (b) 28 (c) 20 (d) 21
  2. 2.What is the distance between the points (3, 20) and (11, 5)? (a) 23 (b) 289 (c) 18 (d) 17
  3. 3.In which quadrant does the point (−8, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  4. 4.In which quadrant does the point (−8, 9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  5. 5.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  6. 6.In which quadrant does the point (−7, 3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  7. 7.In which quadrant does the point (9, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  8. 8.What is the distance between the points (7, 9) and (22, 1)? (a) 18 (b) 289 (c) 17 (d) 23
  9. 9.What is the distance between the points (4, 7) and (16, 16)? (a) 21 (b) 225 (c) 16 (d) 15
  10. 10.In which quadrant does the point (3, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  11. 11.What is the distance between the points (7, 3) and (11, 0)? (a) 5 (b) 25 (c) 7 (d) 6
  12. 12.What is the distance between the points (9, 3) and (15, 11)? (a) 14 (b) 100 (c) 11 (d) 10
  13. 13.In which quadrant does the point (2, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  14. 14.What is the distance between the points (5, 21) and (13, 6)? (a) 289 (b) 23 (c) 18 (d) 17
  15. 15.What is the distance between the points (5, 6) and (17, 15)? (a) 15 (b) 225 (c) 21 (d) 16
  16. 16.In which quadrant does the point (9, −5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  17. 17.What is the distance between the points (1, 12) and (13, 7)? (a) 13 (b) 14 (c) 17 (d) 169
  18. 18.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  19. 19.What is the midpoint of the line joining (8, 6) and (14, 12)? (a) (9, 11) (b) (3, 3) (c) (11, 9) (d) (22, 18)
  20. 20.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
  21. 21.What is the distance between the points (3, 4) and (6, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  22. 22.What is the midpoint of the line joining (1, 3) and (7, 1)? (a) (3, 1) (b) (2, 4) (c) (4, 2) (d) (8, 4)
  23. 23.What is the distance between the points (9, 8) and (18, 20)? (a) 21 (b) 16 (c) 15 (d) 225
  24. 24.In which quadrant does the point (1, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  25. 25.What is the midpoint of the line joining (1, 13) and (3, 3)? (a) (1, 5) (b) (4, 16) (c) (8, 2) (d) (2, 8)
  26. 26.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
  27. 27.What is the midpoint of the line joining (5, 22) and (13, 10)? (a) (9, 16) (b) (4, 6) (c) (16, 9) (d) (18, 32)
  28. 28.In which quadrant does the point (−7, 1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  29. 29.What is the distance between the points (6, 0) and (22, 12)? (a) 400 (b) 21 (c) 20 (d) 28
  30. 30.What is the distance between the points (7, 13) and (22, 5)? (a) 289 (b) 18 (c) 23 (d) 17
  31. 31.In which quadrant does the point (4, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  32. 32.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  33. 33.What is the midpoint of the line joining (7, 1) and (17, 11)? (a) (5, 5) (b) (24, 12) (c) (12, 6) (d) (6, 12)
  34. 34.What is the distance between the points (0, 8) and (15, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  35. 35.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
  36. 36.In which quadrant does the point (1, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  37. 37.What is the midpoint of the line joining (1, 7) and (5, 9)? (a) (2, 1) (b) (8, 3) (c) (6, 16) (d) (3, 8)
  38. 38.What is the distance between the points (5, 8) and (13, 14)? (a) 11 (b) 10 (c) 14 (d) 100
  39. 39.What is the distance between the points (8, 15) and (13, 3)? (a) 17 (b) 13 (c) 169 (d) 14
  40. 40.What is the midpoint of the line joining (2, 15) and (14, 5)? (a) (8, 10) (b) (6, 5) (c) (10, 8) (d) (16, 20)

Answer key

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

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