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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 802 · 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 (1, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  2. 2.What is the distance between the points (1, 2) and (6, 14)? (a) 17 (b) 169 (c) 13 (d) 14
  3. 3.What is the midpoint of the line joining (9, 6) and (15, 2)? (a) (4, 12) (b) (3, 2) (c) (24, 8) (d) (12, 4)
  4. 4.What is the distance between the points (2, 9) and (6, 6)? (a) 25 (b) 6 (c) 7 (d) 5
  5. 5.What is the distance between the points (6, 8) and (9, 12)? (a) 5 (b) 6 (c) 25 (d) 7
  6. 6.In which quadrant does the point (6, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  7. 7.What is the midpoint of the line joining (0, 6) and (8, 16)? (a) (4, 5) (b) (8, 22) (c) (4, 11) (d) (11, 4)
  8. 8.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  9. 9.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  10. 10.What is the distance between the points (1, 10) and (9, 4)? (a) 100 (b) 14 (c) 10 (d) 11
  11. 11.What is the distance between the points (7, 8) and (14, 32)? (a) 25 (b) 625 (c) 31 (d) 26
  12. 12.What is the distance between the points (1, 9) and (4, 13)? (a) 7 (b) 25 (c) 6 (d) 5
  13. 13.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  14. 14.What is the distance between the points (1, 1) and (4, 5)? (a) 25 (b) 6 (c) 7 (d) 5
  15. 15.What is the distance between the points (7, 14) and (12, 2)? (a) 169 (b) 17 (c) 14 (d) 13
  16. 16.What is the distance between the points (9, 9) and (17, 24)? (a) 289 (b) 23 (c) 18 (d) 17
  17. 17.What is the distance between the points (6, 16) and (18, 7)? (a) 21 (b) 15 (c) 225 (d) 16
  18. 18.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  19. 19.In which quadrant does the point (−4, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  20. 20.What is the midpoint of the line joining (3, 17) and (9, 5)? (a) (6, 11) (b) (3, 6) (c) (11, 6) (d) (12, 22)
  21. 21.What is the distance between the points (7, 6) and (14, 30)? (a) 26 (b) 31 (c) 625 (d) 25
  22. 22.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  23. 23.What is the midpoint of the line joining (5, 4) and (15, 0)? (a) (10, 2) (b) (2, 10) (c) (5, 2) (d) (20, 4)
  24. 24.What is the distance between the points (7, 9) and (10, 5)? (a) 25 (b) 7 (c) 6 (d) 5
  25. 25.What is the midpoint of the line joining (1, 0) and (3, 2)? (a) (1, 1) (b) (2, 1) (c) (1, 2) (d) (4, 2)
  26. 26.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
  27. 27.What is the distance between the points (2, 3) and (18, 15)? (a) 21 (b) 400 (c) 20 (d) 28
  28. 28.What is the distance between the points (5, 3) and (9, 0)? (a) 7 (b) 6 (c) 5 (d) 25
  29. 29.In which quadrant does the point (−2, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  30. 30.What is the distance between the points (8, 1) and (16, 16)? (a) 17 (b) 23 (c) 18 (d) 289
  31. 31.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  32. 32.What is the distance between the points (9, 8) and (13, 5)? (a) 7 (b) 5 (c) 25 (d) 6
  33. 33.What is the distance between the points (0, 7) and (15, 15)? (a) 289 (b) 17 (c) 18 (d) 23
  34. 34.What is the distance between the points (1, 27) and (8, 3)? (a) 31 (b) 25 (c) 625 (d) 26
  35. 35.What is the midpoint of the line joining (5, 13) and (11, 7)? (a) (16, 20) (b) (10, 8) (c) (8, 10) (d) (3, 3)
  36. 36.What is the distance between the points (2, 0) and (10, 15)? (a) 18 (b) 289 (c) 17 (d) 23
  37. 37.In which quadrant does the point (6, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  38. 38.In which quadrant does the point (2, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  39. 39.In which quadrant does the point (−7, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  40. 40.What is the midpoint of the line joining (9, 8) and (13, 0)? (a) (4, 11) (b) (2, 4) (c) (22, 8) (d) (11, 4)

Answer key

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

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